Apartment rentals

Elaine, let me make a suggestion. When you find an apartment that looks interesting, go to google maps and check the walking time to the center of things. Old Town in Prague or sort of mid point on Kärntner Straße in Vienna for instance. Then check the transit time.

Then if that looks reasonable, go to the street view and take a look around the neighborhood; and even the route to the center of the tourism.

Remember that each of the cities you are visiting is completely different. Some, like Vienna, are very prosperous, Prague is very young and energetic and Budapest in many ways is still pulling its self out of communism. Krakow I can’t speak to. But I get the impression a cross between Prague and Vienna.

Thanks to the internet you can do a pre-game run through and know what to expect.

Try booking.com and VRBO.
Use their filters for location, price and type of rental.

I stayed in this Airbnb flat in Vienna (wonderful flat in center, hosted by Ursula) in September 2015 and was very happy with it. It is an easy 5 minute walk to Stephansplatz. The owner lives in a flat on the same floor of the building. My review is posted on the site.
https://www.airbnb.com/rooms/2610702?sug=51

In Krakow, I stayed at the Venetian House Aparthotel back in 2012. I was in a small studio with a kitchenette. The location is great (it is right on the main square) which means a room overlooking the square can be noisy. If you look at this place, read the room descriptions closely. The descriptions indicate whether there is a lift and whether the room overlooks the square or a courtyard.

http://www.venetian-house.com/#all

We stayed here in Vienna, not sure the district? But we liked it!

https://www.vrbo.com/533816ha

In Prague we had a hard time with a vrbo as we were arriving Xmas eve... we ended up at Hotel Salvator which we liked, we had a suite with 2 bedrooms and a bathroom in between. Very nice and convenient!

Yesterday's issue of Le Parisien had a front-page article about the mounting crackdown on AirBnB, VRBO/HomeAway, Abritel as well as all the other internet platforms.
Hotel lobbyists have been successful in putting pressure on the government to act, the Mayor's Office has added more agents to verify the dossiers - 500 were dealt with last year, 600 so far this year - and discussions are proceeding more swiftly than before.
I'd expect to see more apartments pulled off the market in the near future.

In Prague we used Residence Arcadia and in Vienna we used Pension Sacher. Both are professionally managed with multiple units. Both are still top reviewed on Tripadvisor. I can't link them to you as I'm working from my iPad and I'm an idiot with it:)

Thanks to all who posted replies or suggestions. I've found good bookings in Budapest and Vienna and making progress on Prague and Cracow.