Use the mass transit systems in Europe, it's the easiest way to get around. I'd probably honestly pass on doing too many things like museums/zoos/etc. These become largely "samey" after a while, but if you can visit palaces and historical monuments I'd go for that.
Check out the Sex Museum in Amsterdam, that's good for some fun. Hell, check out one of the ladies in Amsterdam too, lol. Boat tour on the Sienne river in Paris is something I'd reccomend, really enjoyed that. Even though it's touristy, Eiffel Tower is worth seeing, I'd reccomend going a little bit before sunset, so you can see it in the day and then also at night when the lights come on. In London check out the Tower of London and London Bridge, there's a ton to see there.
You like are going to hit a wall of exhaustion at some point your trip, that's ok.
Take lots of photos, not so much of the tourist attractions themselves, but of you and your buddies. You will appreciate those photos later on.