Definitely sleep in the Alps. Interlaken is near the Alps, but not in it, so you need to stay either in Lauterbrunnen, Murren, or Gimmelwald. We were there a few weeks ago and we stayed in Gimmelwald. It is just down from Murren. There aren't many accommodations in the town, but the scenery is amazing. You can read more about it
here. We stayed at
Pension Gimmelwald. It was creaky and the ceilings were short, but the views were amazing. We were there for two nights and one day. We took the cable car to the top of the Schilthorn, where there is a restaurant and a gift shop. The James Bond movie
On Her Majesty's Secret Service was filmed there. We then took the cable car down to the next stop (called Birg) and hiked back down to Gimmelwald from there. The snow was too high to hike down from the top, and we still were in knee-deep snow in some places from Birg. It was beautiful and probably the biggest highlight of my trip.