Lucerne is beautiful and worth it. We didn't go there last time I was in Switzerland, but went there when I was in HS. If you go here, I would recommend going up Mount Pilatus. Amazing view (if it's a clear day) and the ride down the mountain is beautiful.
Geneva was OK, but Zurich was pretty awesome. One of my old co-workers (French guy) has lived there for the past 10 years and took a couple of days off and showed us around and took us up to Schaffhausen and
Rhine Falls.
Interlaken is also a very beautiful place.
I haven't been to Zermatt, but we did go to Saas-Fee with my wife's friend who lived there, and it was beautiful. Quiet little town that's 100% walk able as cars aren't allowed. They do have these little golf cart things to get around, but they're not really necessary.
I would highly recommend a Swiss Pass for the entire time you're there. Public transportation is awesome in Switzerland and they do enforce the rules on tickets. If you're caught without one, they will make you buy one and then make you pay your fine right there. I saw this happen many times.
If you have a Swiss Pass, I would plan a day to just hit up multiple places throughout the day. On our way from Geneva to Zurich (where we each had friends we were visiting), we stopped off at Thun and Bern and walked around the city for a few hours.
Just be prepared for sticker shock. Everything is uber expensive in Switzerland. A quick lunch at a restaurant will cost you $30-40/person US. Our first day in Geneva, we grabbed a burger and it cost more than the nice dinner we had in Paris the night before. We got to the point that we would grab pre-made sandwiches, chips, and a bottled drink at Coop Supermarket for like $10/person and take them with us on the go, and honestly, because of the fresher ingredients over there, they tasted better than many sandwich shops here in the States.