A lot of Americans think of European travel as a really far away and exotic thing that only those that have a small fortune can do, but nothing’s further away from reality: backpacking across Europe can be really inexpensive depending on which countries you want to visit.
“Fancy”, “glamourous” countries like the United Kingdom, France, Germany, Switzerland, Spain, and Portugal will definitely be on the expensive side if you don’t know how to budget, but there are plenty of trips to keep this trips on the cheap too: instead of renting an Airbnb you can look into a “work away stay”, where you will be able to stay with a local for free (and you might even get paid !) if you are willing to do some light work.
Using local public transportation and visiting the local farmer’s market will also help you stay within budget. Also, be careful about the nightlife in those places, as there are plenty of tourist traps that will overcharge tourists!