Good choices - Rome and Switzerland are possibly my two favourite places in the world.
A great little town in Switzerland is Interlaken - nestled in the hills between two bright blue lakes, great activities nearby in the hills and lakes.
Just out of Interlaken is Lauterbrunnen, which is a little valley between some really big mountain ranges, with massive waterfalls every hundred metres or so.. A beautiful place (do a google images search for Lauterbrunnen). A quick cable car up into the mountains takes you to a place (I forget it's name) where they filmed a large part of the Bond movie "On Her Majesties Secret Service". If the weathers good, you get great views of the alps, and the valley below from the cable car.
In Rome you can't go wrong with food - but the best bet is to avoid anywhere that speaks english or provides an english menu. You'll pay half the price, and the food will be as good or better.