Which cities should I visit to extend a Berlin trip?

I have booked a 2 weeks trip to Berlin with my partner, flying in and out of the city, in early August.

We have booked accommodation for most of it and left room for 4 days to explore outside of Berlin. From what I've read our realistic options are: Munich, Dresden & Leipzig, or go to Prague perhaps.

Wondering what you think is the best choice? I think after Berlin, a nice relaxing destination with some nature options with be nice. We are trying to be budget conscious.

I was interested in Munich due to it's proximity to the alps and some castles, but from what I've read it's another 3 hours of travel to get there, so wondering if that's really all that convenient. My co-worker from Munich rated it highly as well for a summer destination.

I'd be happy to visit some other German towns for a different flavour, and familiar with lots of music that has come from Dresden and Leipzig, so open to that.

Prague is a good option for variety, but might be a bit of a travel nightmare given we need to be back in Berlin to fly out of.