Should I visit Berlin > Vienna > Budapest?

I’m planning a trip to Europe this spring (April/May) and I’m thinking of going to Berlin, Vienna, and Budapest. I’d like some advice from you fellow travelers:
1) Do you think those 3 cities would make for a good trip or could you suggest something better? I absolutely loved Munich and want to visit Germany again, hence why I chose Berlin. The other two cities I picked because I’d want to visit them some day (and by general vicinity), but they’re not a must. I could fly cheaper to Dusseldorf or Frankfurt, but I honestly don’t know much about those two besides chocolates.
2) If I stuck with those 3 cities, what are the must sees in each? I’m planning on spending 4 days in each. I think I’d want to catch the Vienna Boys Choir perform (or is that overrated?) and visit the biggest bath in Budapest.
3) I’ll be traveling alone to Europe for the first time. The other times I’ve gone, I wasn’t traveling alone. So, I want to try something different like finding a host family, staying with them, and getting to see the city through a local’s eyes. How do I go about doing that? Or are any of you in the cities I mentioned above and would like to show me around?

Thanks for any advice you can give!