Hi, me and friends are doing a speed-tour through Europe for spring break. We only have one day per city. I know this sounds crazy but it's being done! We're starting out in Zurich but realized it is crazy expensive so I found out about a little town called Rapperswil which looks really cute and is very affordable. Does anyone have ideas or advice about what to do while in Zurich and Rapperswil? Then we move on to Appenzell, which has a little cheese factory in it, so that should keep us busy but I always appriciate advice or suggestions. Then we move to Mauren, in Lichtenstein...which I have regretfully heard it boring, so if anyone wants to speak up on why it isn't boring and what to do while there besides hike (which we'll have plenty of chances to do EVERYWHERE). Thanks so much, I have never been to these places so that's why I was wondering what there is to do.

You might want to give a little more info so others can be of assistance. Things like:
1. How many days do you have?
2. Where are you flying back home from--Zurich?
3. What is your budget for accommodations?
4. Do you want lots of snow for skiing or open ground for hiking?
5. Are you into museums or just outdoor things?

With only one day in each place, less the time it takes you to get there, you really don't have an issue about what to do. You arrive, you wander about town and take in the local atmosphere, have a meal or two, then move on.
Yes, Rapperswil is a cute town with some nice restaurants and some very pretty buildings. Appenzell is charming, once you get past the cow smell. Their cheese is wonderful. There is little to do in Lichtenstein except look at and buy stamps. But you won't be at any of these places long enough to get bored.
I'm curious why you chose these places and then ask what there is to do? Usually I thought a person chooses a place to go because of WHAT they WANT to do there.

Raperswil is a very small town about a half hour by train from Zurich. IMO, it is not a good base to use to see Zurich. You can see the tourist bits of Raperswil in about an hour. It it much better in early summer when all the gardens are in bloom, it will be cool to cold in March and April. (I live in Zurich and it is 0 C today and there is snow on the ground.)

If you only have one day, you might want to skip Zurich and spend more time in the Alp areas. You cannot see the Alps from Zurich unless it is very clear. Zurich is very pretty and on a nice lake, but your tour is so rushed I am not sure it is worth your time, esp in the early spring when the weather will not be very nice. You are better off in the Alps where you have a better chance of clear weather.

I've stayed overnight in Appenzell which is a very small, but totally quaint village. I think Patrick's problem with the smell probably came because he stepped in some.
I would recommend, and only if you enjoy such things, also taking a look at the world-famous library and abbey church in very nearby St. Gallen. The library interior has to be seen to be believed and the interior of the church has repeatedly been labeled as "the most beautiful" in all of Switzerland.

Appenzell has some great area hikes over gently rolling hills (no mountains here)-yes cows predominate, and so do their smells. Urnasch (15 mins from Appenzell) has a 4-story home that houses a great country museum. Urnasch also has but connections up to Mt. Santis, the area's tallest peak (gondola from final bus station). Not too expensive, and worth it IMHO.