Berlin is very rich with museums and historic sights, but the city itself doesn't look too much like Old Germany. If you want to see fabulous indoor sights, you'll have plenty to do if you stay in Berlin.
As for Prague and Munich, I'm of two minds: Both have historic architecture appealing to visitors, but two days would be quite a short time in Prague. I might be inclined to choose Munich for that reason. The train trip takes roughly 4 to 4-1/2 hours. On the other hand, Prague's historic center--though very touristy--is drop-dead gorgeous; everyone should see it at least once (and I don't think Munich rises to that level). Trains to Prague run somewhat less frequently but generally take just over 4 hours. That's a fairly substantial extra travel leg when you're just figuring out how to spend two days.
Because of its location, Florence suffers from extremely hot summers, with miserable weather potentially extending well into September. My preference would be to see it a bit later in the year or in the spring, but you'll be there anyway, for the wedding, and we're only talking about two extra days in the area. You use the Search box on this website to take a look at September weather in nearby cities. Check several years to get a reasonably decent idea of what you might run into.
Florence weather -- September 2023 (September 2024 was nowhere near as bad.)
At a glance Siena looks similar to Florence, weather-wise, at that time of year. Bologna's marginally less scary. Pisa and Lucca look a great deal better to me for a September trip, just considering temperatures.
I like Berlin's offering of lots to see, almost certainly not-hot weather and no need for an extra travel leg, but all your options are good (with the weather caveat).
