DACH - Deutschsprachige Community für Deutschland, Österreich, Schweiz

You're correct about Heidelberg – at least as far as socializing and learning together go. You may occasionally need to speak German when you're shopping or what not. By extension, the experience should be similar (although not quite as pronounced) in most other university cities with a similarly high proportion of students and university alumni. Finding a place to live will be a challenge though, and rather expensive.

In every major city you’ll find communities which will speak only English. But from my experience these are mostly “expats” staying for a few years and leaving again. If you like to stay forever and want to make friends which will be close for an extended amount of time I recommend naturally meeting people, no matter their language. Most Germans I know (Gen X and Millennials) speak sufficient English to converse. In a mixed group it might happen that you will switch languages and you’ll learn it naturally especially if you already have some basic skills.

A thought on Berlin: while it's relatively easy to live there speaking just English, there is a big "expat bubble" that, in my experience, doesn't really interact with the locals. As a local, I've always found that a bit sad

Any given university town has Erasmus parties. Also, there are some universities with a heavier focus on international programmes and the cities with such units do have a higher density of english speakers.

Berlin is the only place in Germany where I sat down in a restaurant and was approached by the waiter in English before switching to German.

Berlin for sure. In my experience, most major cities in Germany have international islands, where speaking English is the default, but they quickly get more provincial and less welcoming to non-Germans once you move off of that island. Berlin is special in that even the old-school parts of the city often don't feel that way (the suburbs still do though). Hamburg may be a close second.