Did that last year. Engelberg has a cable car (end of the road, almost) that runs up to Brunnihuette (hotel/restaurant right at the station) and the trail to Rugghubelhuette. About a 3-4 hour hike with beautiful views and mountain goats. Even a gate with a sign that read, I forget the German, but 'please don't let the goats out'--with no clear way tell which side they should be on.
Information on the huts:
Information on the cable car: (top one for Brunni')
Good choices all around. Whatever you choose will be great.
I had strep. We visited the doctor around 10:30 on a Saturday morning. He was away on a house call briefly while we waited sand, including that time, it was about 45 minutes from the time we arrived and the time we left. And we walked out with three prescriptions in my hands for $147. Not cheap, but We were very happy. And the exam room was IN the doctor's office. He took our history on his computer and we filled out a card with no more information than a hostel would require. Fairly amazing.
Lucerne is a good place to visit, too. Lucerne is great for a big city in that it isn't really a big city. It's a college town--come at the end of exams. They are crazy :). Good pizzeria with gluten free pizzas--if you need it it is a lifesaver.