I'd pick Interlaken as a base over the towns on Lake Geneva, but that's because I'd value the in/on-the-mountains and small town experiences over the nightlife/on-the-lake experiences for which the lake towns have an advantage. How about three nights in Montreux and two nights in Interlaken?

Also, if you want to get to Rome by train in 3 hours, consider taking an overnight train. Since you'd be sleeping anyway, you'll essentially get to Rome without losing any sightseeing time at all. Be aware, though, that if you only pay for a second-class couchette overnight, you'll have only very limited resources for freshening up upon arrival in Rome. For that purpose, it might be worth springing for a first-class sleeper, or perhaps for finding a hotel in Rome that will allow early check-in.