If you’re an international student (or any student really) at Heidelberg University then you can go on super inexpensive “excursions” around Germany.
The day-trips cost about 16-25 euros each and include transportation, a tour guide (who will only speak German), and the entrance fee to select attractions. There are also longer weekend trips, such as one to Bavaria and another to the Baltic Sea. These are understandably more expensive as they include dinner, breakfast and lodging.
I personally loved the excursions, especially the day-trips!
For the day-trips, don’t worry about going with people you’ve already met. I met some of nicest people on the trips (so I never had to eat or spend downtime alone) and even some of my closest friends abroad.
The weekend trips are a bit different, since you have to share a room with people. For those I preferred going with at least one person I already knew.
My favorite excursions included Bavaria (a weekend trip), Marburg and Tübingen/Hohenzollern.
I honestly wish that I had done more of them. However, I think that the university excursions might be less enjoyable if you don’t understand much German, as the tours are conducted entirely in German. That being said, if you go with friends or are not particularly interested in history then the excursions would still be fun.
The only excursion that I personally wish that I hadn’t gone on was the four day trip to the Baltic Sea. It was a 9 hour ride (at least) to and from and the weather was really rainy when I was there. I also live by the ocean here in the US so the lighthouses and beaches weren’t nearly as exciting for me as they were for my Austrian friend.
As a student studying in Germany, I thought it was more important to travel around Germany rather than around all of Europe. The excursions really let me do that without breaking the bank. I got to see the Bavarian Alps, Neuschwanstein, the Swabian Alps, a Roman fort and chalk cliffs.