I don't know your major, but I had several opportunities to travel for field work and conferences in college as a geology major. I applied for research grants from my school to have costs covered and to get paid in some cases ($10/hour, up to 40hrs/wk). I ended up in Europe twice, and both times I was able to set my return flight later than needed so I could travel independently (anything on my own was out of pocket). Other trips were within the US. I was a pretty mediocre student, just got lucky with opportunities and never let one pass. A history major friend got to England for a conference, a studio art friend to China, and a physics friend to Germany, so with some initiative, it's possible, regardless of what you study.

I also studied abroad for a semester and traveled quite a bit then. I put A LOT of time into tracking flight costs to various places, snagging cheap ones with budget airlines, and finding well-rated hostels for <$15/night. I ate shitty grocery store sandwiches and kept my food budget around $8/day. I also very rarely used public transportation in cities and stuck to walking. I spent a month in the France/Belgium/Netherlands area for under $1000, paid for with my field work earnings.

You could also look into things like WWOOF for free accommodation and food.