1 Month Europe Trip Recommendations / Tips?

Hey all, I'm starting to plan a 1-month backpacking trip around Europe after I graduate and before I start a full-time gig. The trip would be from late May into June. Any recommendations for must-hit cities while overseas? Places to avoid? Looking to spend 3-4 days in each city/country to cover as much ground as possible but also get a decent sense of where I am at. I want to hit the classic spots like London and Paris but also would really like to go off the beaten path if you all have good recs for some underrated cities. A younger social scene is important, but I am also interested in history/culture/sports etc. Appreciate any and all input.