Mt Rainier NP
Mt Rainier is an incredibly photogenic mountain, and the surrounding national park is well worth a visit. There are two main areas in the park: Paradise and Sunrise. As such, I recommend spending two days in the park, ideally doing a day hike in each.
View from Summerland
View from Panhandle Gap
Sunrise area:
The Sunrise viewpoint is remarkable and worth a stop. The day hike I did and would highly recommend is the Summerland/Panhandle Gap trail. It starts at a small trailhead early on the Sunrise Rd (so get there early (before 7:30 a.m.) when visitors abound, such as in July-August). It is a 10 km (one-way) hike with a 900 m elevation gain that starts in a moody forest and follows a creek upwards (offering some nice glimpses to the south now and again) before reaching some beautiful alpine meadows and finally reaching Summerland. This part alone (around 6 km one way) is worth the hike. The views of Mt Rainier from the meadows are remarkable. The trail continues upward through a rocky terrain with a beautiful lake before reaching Panhandle Gap, which offers amazing 360° views. Note that the very last climb to the gap might require crossing a slippery snow field. It is, in my opinion, not as scary as it looks and doable without microspikes or poles. This is one of the most beautiful hikes I've done in my life, and I highly recommend it.
View of Mt Rainier from Paradise
Mt Rainier from the top of the Skyline Loop
Paradise area:
East of Paradise proper, the Reflection lakes offer an incredible view of Mt Rainier early in the morning (between 6 and 8 a.m. depending on the season).
In Paradise valley, there are many short trails (some paved) with beautiful views of Mt Rainier. If you don't have much time, the view from Myrtle Falls is very nice. The main attraction of the Paradise area is the Skyline loop trail. This 9 km loop culminates near aptly-named Panorama point and offers incredible views of the whole mountain range (you can see as far as Mt Hood in Oregon when the weather allows it). I recommend doing the loop counter-clockwise for a gentler ascent. There are different shortcuts to parts of the trail but I advise doing the full loop unless you're really short on time for the full experience.
Olympic NP
The Olympic peninsula, which is mostly comprised of the national park, astounds by the diversity of its landscapes. To get a glimpse of all the biomes of the park (mountain lakes and forests, high mountain ridges, Pacific coastline and, perhaps most suprisingly, temperate rainforest), I recommend spending at least 3 days in the park: two in the north (Port Angeles is the natural base of operations) and one in the west (Forks is the default choice, although I was shocked at how expensive the hotels there were).
The view of the Olympic mountain range from the top of Mt Angeles
View of Mt Angeles in the early morning
Hurricane Ridge area:
A paved road from Port Angeles leads to Hurricane Ridge, which offers an already astounding view of the Olympic mountain range. There are some easy and paved hikes to Hurricane Hill which offer some more vantage points, and you can hike an arbitrary portion of the Klahane Ridge trail to get more views in, but the hike I personally did was a variation that lead to the top of Mount Angeles, which offers incredible 360° views. To get there, follow the Klahane Ridge trail for about 3 miles, then follow the steep trail through the forest at the intersection for about 2 more miles. There is some rock scrambling at the end that can be quite challenging, but if you keep going as left as possible for as long as possible, you can avoid nearly all of it and relatively easily make your way to the summit. If you're uncomfortable with rock scrambling and/or suffer from vertigo, this might not be an advisable hike.
Sol Duc and Marymere falls
Lake Crescent/Sol Duc/Elwha area:
Lake Crescent is a beautiful mountain lake to the west of Port Angeles that is worth a stop. There are three hikes worth doing around it: the Spruce Railroad Trail circumvents the lake from the north-west side and offers nice lakeside views. Pyramid Peak Trail was recommended to me to get a beautiful view of the lake and the surrounding mountains but because the clouds were very low on the day I was there I decided not to bother. Finally, the short hike to Marymere Falls is worth it as both the falls themselves and the walk to the forest to get to it are very nice.
Not far from Lake Crescent, the Sol Duc area is worth a stop. The main attraction is a short (about 2 km one way) walk to the Sol Duc falls. Again, the walk is almost as nice as the falls themselves.
The last interesting part of the park nearby is Elwha Valley. Because of a landslide, most of the area is not accessible by car but requires a rather long hike.
Views from Rialto Beach
Pacific coast area:
There are multiple beautiful beaches you can either stop by to enjoy the scenery or along which you can walk along.
Ruby beach is a famous one and worth a short stop, but my favorite one was Rialto Beach and the walk along it to Hole-in-the-Wall (about 2 km one way). At low tide, you can see some nice sealife in the tide pools along the beach. The dead trees and beautiful rock formations in the water make for a very unique, desolate landscape that I highly enjoyed.
Another hike that I recommend if you have the time is the Ozette loop. This hike is an equilateral triangle starting at Ozette lake with 5 km-long edges. Two edges are wonderful walks through the forest, mostly on some cool boardwalks, and the last edge consists in following the coast. A few passages might be awkward at high tide. I recommend going clockwise if you do the loop in the morning to get better views on the coastside. If you're lucky, you might end up seeing a lot of various wildlife. I saw many very placid deer, some snakes, heard some sea lions and even saw a young black bear from a safe distance!
Hoh Rainforest
Hoh Rainforest area:
This is a very unique place (which attracts a lot of visitors - expect to wait 1+ hours at the entrance if you get there late on a busy day) which is one of the rainiest places in the world (mostly in the winter). The rainforest really comes alive when it rains (what a suprise) so do not hesitate to go there during or after inclement weather. There are two short trails (Hall of Mosses and Spruce Nature trails) that are both worth it. The moss-covered trees make for a unique environment. If you're lucky, you might some cool banana slugs! Finally, you can follow the Hoh River Trail for as long as you like (it's over 20 km long), but there are two nice places to get to the water proper and enjoy the beautiful river views, one 1.5 km in and the other 6 km in.
North Cascades NP
Located near the Canadian border, this remote national park is a hidden gem you have to work for in order to fully appreciate it. Apart from the (beautiful) Diablo Lake with its characteristic color and surrounding overlooks, most of the park's beauty is hidden behind day hikes with significant elevation gains. The views from above, however, are definitely worth it.
Diablo Lake from the eponymous overlook
Diablo lake area:
Diablo lake itself is very beautiful and the main attraction for "casual" visitors of the park. Diablo Lake overlook on SR-20 offers the best views of it. Thunder Knob trail (6 km roundtrip with 130 m of elevation gain, quite easy) offers another nice perspective on the lake. Other overlooks along SR-20 are also worth a stop. Another hike I did in the area is the Pyramid Lake trail. Despite its deceptive description on the NPS website (moderate, 7 km roundtrip, 450m elevation gain), I found it to be surprisingly tough, with a nearly constant relatively steep climb. The lake itself is very peaceful and pleasant.
Sahale Arm from the ridge below
The amazing panoramic view from the top
The view from Maple Pass
North Cascades mountain range:
I did two one-day hikes in the North Cascades proper (even though the second one is technically outside the park border for most of its length) that I highly recommend.
The first one is the Sahale Arm Trail through Cascade Pass. It's a strenous day hike (19 km round trip, 1200m elevation gain) but the views are totally worth it. The trail begins at the end of Cascade River Road (37km road from Marblemount, last 16 km are unpaved and can get a bit rough). Unless you get there extremely early, you might have to park on the road because the parking lot fills up extremely quickly. From the trailhead, it's an unexciting gradual climb through the forest for about 4.8 km with 36 switchbacks (protip if you want to spend your time counting them: it's better to count down rather than up to make it more interesting). After the switchback section, you quickly get to Cascade Pass, which offers some nice views already. If you keep going, you'll alternate some tougher switchbacks with less strenuous ridge sections with beautiful views (Doubtful lake on the right is magnificent) before reaching a final tough climb that will lead you up the Sahale Arm to the bottom of the Sahale glacier. The panoramic view from the top is mindboggling and well worth the effort. Note that charming mountain goats abound on the trail.
The second one, which starts outside the park to the east, is called the Maple Pass loop (also referred to as the Heather Pass loop). It begins at the Rainy Lake trailhead on SR-20 and it's a moderately strenous hike (11.5 km roundtrip, 615 m elevation gain). Since it's a loop, you can do it clockwise or counterclockwise but I heavily recommend the latter unless you're superfit or willing to go very slowly because you'll have a very tough and steep climb ahead of you, whereas the counterclockwise direction offers a more progressive climb. The offshoot trail to Lake Ann about 1.5km in is nice, but not unmissable: the real draw here are the views from the top of the ridge in all directions. This hike's variety in terms of landscapes traversed and seen is also remarkable, with the view of the snowy main Cascade chain being the definite MVP.