Apart from the famous tower and some museums is there much to do in Pisa? Would it be best as a day trip from somewhere close, or perhaps as a 1-2 night stop off?
If you have time to do it I would recommend an overnight stay. There are some magnificent churches to see, as well a the usual attractions. Pisa is only an hour from Florence on the train, which makes it a really convenient side excursion.
I believe one day is enough in Pisa. You will want to spend the night and then head out. There is enough to do for one day, but that is about it unless you want to go to the near by outlets and spend and extra day.
One night is more than enough and to be honest if you are in Florence I would do a day trip instead. I only stayed in Pisa as we were flying out from Pisa and I was a little bored after I had seen everything. It's enough for a day or even an afternoon, it's pleasant to walk around, but compared to Florence where you have too much to choose from, you are better off there to have dinner.
Well, if sightseeing is all you do during that day, I guess one day is enough, but you must check whether the museums and such are open on that day, it would be really bad if you turned up on a day when some are closed ^^. I guess it all depends what you want to see and how many attractions - if you make a good route and then follow it, you might even save some time, who knows.
Best time to go is the end of june. Last saturday of june every year they perform the Gioco del ponte, their kind of Palio. http://www.giocodelpontedipisa.it/ Then July 2 you can move to Siena and see the real Palio. http://www.ilpalio.org/index_english.htm