tufbuf, thanks for the great trip report. Being a Swiss myself and living just outside of Lucerne, I'm glad you enjoyed your time here!
vacationgrl, Being a local, I'd advise you to spend another day in my great city and go for Mt. Pilatus. You can do a nice roundtrip that features a cruise to Alpnachstad where the station of the cogwheel railway (the steepest worldwide!) is located. Take that train up to Mt. Pilatus and enjoy the great views of Lucerne and the surrounding mountains. For the way down, take the aerial cablecar all the way to the suburb of Kriens. From there, you can ride with the public bus (Line #1) back to Downtown Lucerne. Stop is located right in front of the Schweizerhof Hotel. A lot of tourists do this round-trip and you can also do that in reverse order of course. Check this:
http://www.pilatus.ch/en/railway-cableways/golden-round-trip/
Geneva is a 3 hour train ride away. While it is a nice city as well, it is kinda similar to Lucerne, located on a lake - just a bit larger. I, for my part, would stick to the Lucerne area. Different story if you have friends in GVA though. There are direct trains from Lucerne that run every hour. For about 30 minutes of the ride, your train will reach a speed of 125 mph, which can also be an experience.
In case
ABD does NOT take you back to ZRH airport: The main station of Lucerne is located just across the lake from the Schweizerhof hotel. You can easily walk over or just hop on a bus and get off at the very next stop, since they all serve the train station. From there, there's a direct train to the airport at 10 minutes past every top of the hour. The journey takes around 70 minutes. The U.S. bound flights leave ZRH at around 10am, 2nd departure wave for the U.S. is around 1pm. Should your flight leave around 10am, take no later train than 7:10am. The trains are generally very clean, safe, modern and run on-time almost right down to the second - like a Swiss watch.
Hope that helps. Otherwise, just ask!