With Euro 2008, Switzerland is likely to be very crowded, especially for Zurich, Geneva, and Berne or Basel (? can't remember) where matches are hosted there. May have to get hotel further away from the city and off the tourist places. Usually the Tourist Promotion Board can help with booking hotel and they are found nearby of the railway station.
Lucerne is a nice city but very touristy and will be a lot worse during this time. Those mountain nearby will also be crowded. Imagine all the standard and package tours go to Lucerne and the nearby, Mount Titilis (check spelling).
People come to Switzerland mostly for mountain scenery and this is best done on foot; IE hiking. You can take the train ride to Interlaken (city of two lakes) but stay up in the mountain like Wengen, Murren, Grindelwald or other mountain resort areas. Along the hike, can see beautiful peaks like Jungfra, Eiger and Monch, and lakes. Warning: Can have difficulty getting accommodation during hiking season and weather can be unpredictable as in rain/cloudy/thunder.
Another area to visit will be the Rhine fall (largest waterfall in Europe). Stein Am Rhein is a very beautiful old town.
Do google or check out guide-book. Have fun!