The distance is quite a bit but the plan is to stay at Hotel Krone in Attinghausen and in the morning catch the nearby Gondola to Brüsti (apparently order it by the phone at the lower station by asking “Bergfahrt, bitte” and that’s it.). From here it's still a 20km hike with approx 700m of incline to Engelberg. At Engelberg you can take a lift to Jochpass and then walk a few km's to the high up Hotel Engsltenalp. It will be a big day, especially with the Surenenpass!
(from Altdorf)
Distance: 25.9 km (from Brusti its about 20km)
Minimum Elevation: 449 m
Maximum Elevation: 2248 m
Total climb: 1659 m (about 600m if starting from Brusti)
Total descent: 983 m
Altdorf 452 m 0.3 km / 0h20 Altdorf Bahnhof 449 m 1.4 km / 0h30 Attinghausen 479 m 3.9 km / 2h40 Brüsti 1526 m 5.2 km / 2h50 <--- We start here Surenenpass 2282 m 3 km / 1h00 Blackenalp 1775 m 1.6 km / 0h30 Stalden 1608 m 1.8 km / 0h30 Stäfeli 1411 m 1.1 km / 0h20 Alpenrösli 1264 m 2.9 km / 0h40 Talstation Fürenalpbahn 1083 m 4.7 km / 1h00 Engelberg 1002 m
Distance
Advisable to catch the seilbahns up as far as is required, this will reduce the elevation gain by about 1200m and distance by about 6km (see interactive map: http://www.titlis.ch/en)
Cable car cost as at 2017 (einweg or one-way):
Looks like there is an Engelberg - Jochpass 33 CHF, well worth it, not sure if this is just the bundle price. I couldnt see a direct trip on the map so I think it is a 3-4 stage hop like below:
If staying at Flüelen etc consider taking a bus to the starting point. From Flüelen, Hauptplatz
401 to Attinghausen, Seilbahn (Cable car), takes about 20 mins looks to have 1 changeover at either the central Altdorf (Altdorf UR, Telldenkmal) or Altdoft Bahnhof.
Most walkers take this in 2 days since there is good accomodation along the way. But could be done in 1 long day, espcailly if starting from above Attinghausen.
From Brüsti its less to travel and from here it easy a 1-day hike.
Stafeli is a great option to stay indoor at the farm. The chapel at Blackenalp is open.
At Surenenpass there is an opened comfortable wood shelter called Schutzhutte
Talstation Fürenalpbahn - Schutzhutte/Surenenpass about 3h
From Surenenpass down to Altdorf there are 2 ways to go down..went off the via alpina and followed water stream
Surenenpass - Attinghausen is marked 3h35
Very good people at the Hotel Krone in Attinghaussen. They did opened their dortoir only for myself on their day off. And they had very good prices too, on August 2011: Dortoir with shower and breakfast, 30 Sf. Or half board for 59 Sf.
If you make it this far then the plan is: http://www.engstlenalp.ch/en/ 76-84 CHF, reserve with credit card but pay cash or Maestro.
http://www.youthhostel.ch/en/hostels/engelberg (6 CHF charge for non-members)
http://www.engelberg.ch/en/accommodation-dining/bed-breakfast/
For Engelberg, try engelberg.ch, or the youth hostel.
We stayed in the Familienherberge, located (unfortunately) a ten minute walk from downtown, and in a neighborhood dominated by drab, modern apartment buildings. The herberge itself, however, is an oasis of Swiss charm. The building is a classic timber chalet, and inside it is unusually neat and clean (even by Swiss standards). Yet once again, we were welcomed warmly, and meals (served cafeteria style) were sumptuous. The place was dominated by families with children, and had a friendly and active vibe. We ended our two-week Via Alpina trek on a pleasant note.