One month backpacking southern europe

Hi everyone!

I am planning a backpacking trip for summer 2026 to southern europe with a friend and I'm looking for some advice.

Our current itinerary:

*fly to rome

*travel by train to florence

*cinque terre

*milan

*interlaken

*nice

*barcelona

*fly out of madrid

My only specific date is barcelona on june 14th for the formula 1 race, so i'm trying to work around that.

My ideal budget is <$5,500 each, including flights. Atm, flights look like they will total to just under $1,500 round trip per person (flying out of central USA). This leaves just over $4,000 for transport, hostels, food, day trips/tourist stuff, etc. We will be staying in hostels the whole trip and, as broke college kids, aren't vying for anything expensive.

I'd love some advice on what to add/remove or just change entirely, as well as packing/things to bring. I know these countries are more expensive than a lot of options (balkans), but these would be my top picks to see.

Any advice is appreciated!