3 months backpacking Europe with 2k solo

2000€ over 3 months is about 20€ a day, which outside of the big cities can probably cover overnighting in hostel dorms and some cheap food from a supermarket, bakery and/or fruit stand. That leaves you nothing to travel and no room for error, but if you don't mind flying a sign or busking and appealing for kickdowns, if you don't mind couchsurfing, if you hitchhike or take overnight buses... should be fine.

Try to avoid the big holiday destinations, especially during the weekends, since there will be less rooms available and the prices anyway will be higher. It used to be that visiting the Med outside the summer holiday season was super chill and lots of quiet/cheap/abandoned places to check out, but i think with climate change and especially this year with the fires it might be that autumn/winter draws more tourists. Maybe try talk to some locals to get the scoop.

Generally Eastern and Southern Europe is cheaper than Western and Northern Europe. The culture is a bit different in each corner of the continent and depending on your personality one place may appeal more than another. Most places have something interesting to see.

You might have more luck finding people who want to help if you share a bit more of your story and plans.