I will not mention the standard tourist destinations like Kotor, Perast, Blue Cave, Budva, as sufficiently described in the internet.
There is a bus stop at the main street with buses app. every 30 minutes to Kotor and Herceg Novi. The theoretic schedule can be found on:
https://www.omio.com/?landing_referrer=https%3A%2F%2Fwww.google.com%2F
Into the mountains:
The road behind Lavender Bay direction Niksic leads you into a different world with beautiful views of Kotor Bay on the way. You will find many restaurants with local farm food at reasonable prices and hiking opportunities.
Another option is the small and at times rough road going up below Lavender Bay past the car park,. This will eventually lead you to Herceg Novi. Ideal as well for morning runs, if you do not mind the steep incline, almost no traffic.
Nevidio Canyon:
2h drive close to the Durmitor National Park. Canyoning is a livetime experience with jumps between 3 m and 12 m (the higher onces can be avoided) not for the faint hearted.
We had excellent experience with below company, where the tours are conducted by professional rescuers, who have climbed most mountains above 7000 m in the world. The tour starts at the Eco Village Nevidio, which is as well a great spot for lunch after the canyoning.
https://canyonnevidioexplorers.com/
Kotor:
If you want to escape the tourist lines , try the ladder of Kotor to get a bird view of the city. the entrance is next to the Scurda canal outside of the old city.
On the way up there is a nice rest place called 'Cheese Shop' , prices a bit on the higher side, but considering the location not unreasonable.