I would suggest staying somewhere in the valley south of Interlaken, I suggest Lauterbrunnen its pretty centrally located, and has everything you need, plus its a good starting point for hikes (and we found a hostel for only 14chf a night).
As for a dayhike I suggest this:
Head from Lauterbrunnen to to Gimmelwald via bus and cable car. From Gimmelwald theres a great long hike that goes to the top of the Schilthorn that should be in great shape during the summer. It also passes through some great little mountain pastures, and further up it gets rough enough to make it interesting (ie sections that have cable to hold on to). Then from the top you can either wimp out and ride the cable car down, or there are many way to hike all the way back down to lauterbrunnen or gimmelwald.
But i definately suggest at least going to the Jungfrau region, either the interlaken side (more touristy) or the Lauterbrunnen side (Less toursity). You could keep yourself entertained for weeks just hiking there.
I found some maps if these help at all, you can get them free anywhere in Switzerland:
http://www.zurich.ibm.com/eurocrypt2004 ... _large.jpg
http://homepage.sunrise.ch/homepage/avo ... te_som.jpg