The essentials are the Ponte Vecchio bridge across the Arno with it's little shops and of course the Accademia Gallery to see the original statue of David. It's a lovely city and not very large so easy to see the important things. Fiesole a village on the hillside overlooking Venice is great for views.
I'm sure jeans will be permissable in the hotel but only the hotel themselves can tell you if they have any rules. I would say however that Florence is a very fashionable city and it is possible to wear jeans and a casual look without looking like a backpacker. The shops are very good - take some money to stock up on Autumn/Winter clothes. Florence is one of the cities that the fashionista's go to to see what's in the shops - along with Paris & New York.
http://www.lonelyplanet.com/worldguide/italy/f lorence/