Best places to go/things to do?

Hey, I’m about to visit Budapest with 3 friends this week for 5 days (Saturday-Thursday). We’re all 21-22 and have never been before.

Can anyone recommend the best places to go and things to do?

Also how much money would you recommend taking? We’re English, so I thought about £200-£250. We’re interested in the nightlife, sights, food and any unmissable activities