ok, i've been to some of the cities you've mentioned... here are some recommendations!
london: the National Gallery is fantastic- be sure to check it out. shopping in Covent Garden is a lot of fun. see a play/musical- you can usually get cheap seats the day of the performance. take a tour of the Tower- it's fun and touristy. be forewarned that pubs close at 11 pm- so find some after-hours bars/clubs if you want to stay up late!
a day trip to oxford or cambridge is really nice- i prefer cambridge, personally.
Dublin: sooo fun! lots of nightlife in temple bar. go to guinness brewery, trinity college, shopping on grafton and o'connell st. do a musical pub crawl. try to take a day trip to see some of the countryside! have a drink at the octagon bar in the clarence.
Paris: so beautiful it will break your heart... i lived in the 5th Arrondisement, and loved it... the Sorbonne is there, it's gorgeous. Sit in the Luxembourg Gardens on a nice afternoon and people watch. Go to the Musee D'Orsay (esp the TOP floor), the Louvre, Picasso and Rodin museums. Buy a baguette and some cheese, and sit on the banks of the Seine. Eat pain au chocolat every morning.
be sure to check out the Marais district as well- it's the Jewish/Gay area. such fun. the Bastille area has lots of fun bars and clubs- a very young area. Go see Jim Morrison's grave. (if you couldn't tell, i ADORE paris!)
Amsterdam: Visit the "coffee shops." 'Nuff said.
no seriously, be sure to go to the Ann Frank museum (very moving), the Van Gogh museum, the Rijksmuseum... Walk around the Red Light district (it's kinda creepy, but interesting). Browse the sex shops. eat waffles at 4 am. it's a good time, but don't stay for more than a few days or else you might never leave...
Prague: this city is GORGEOUS. take a walking tour of the Jewish synagogues- there are some beautiful ones there. Drink absinthe. (it's legal!!! i *almost* tried it... but chickened out!). I was there in '98, and it was starting to get pricy... probably pretty expensive now.
Vienna: Go see an opera. The big art museum (forget the name) is really good.
Venice: sit in San Marco plaza at night (when it's cool) and get a drink at one of the outdoor cafes. Go to the Peggy Guggenheim museum (it;s my FAVORITE museum in the world- it's housed in this beautiful old house on the canal... wow.)
Florence: the Duomo, of course. See the "David"- it's amazing. Buy some cheap leather goods from the outdoor markets. Just take in the beauty of this amazing city...
Rome: St Peter's is breathtaking. Lots of ruins to see. Fantastic, but expensive, shopping around the Spanish steps.
Milan: Not much to see in the city itself... one big church (forget the name). Take a day trip to Lake Como if you have time. it's stunning.
Anyway, those are all the cities i've been to... i'll post more if anything comes to me. Have a GREAT trip, and be sure to post lots of photos when you return...