If you wanted to drive, then:
- US to Budapest, three days in Budapest
- Rent a car and drive through Slovakia to Krakow. Ive done the first
half of the trip and its beautiful and there are a few places worth
stopping. (Banská Bystrica, Banská Štiavnica, Lake Strbske Pleso and
the High Tatras, and a half dozen really beautiful castles).
- Drive to Vienna
- Return to Budapest, drop off the car and spend 3 more nights (this
gets rid of the second country drop off fee on the car)
- Fly home
The issue is the cost.
You said three weeks. Maybe two of that will be with a car. So probably not less than $1500 rental / toll / gas / insurace / parking cost (wild guess) + traffic fines that arrive six months after you get home + rip off auto repair on pre-existing damage + time in the local lock up for hitting a cat. Just the usual. You will have no use for the rental car within Budapest (which is why I say rent it just before you leave town) or within Krakow or within Vienna. But you will pay 30 euro and up each day to park it. You might get some use out of it for day trips out of town, but not really so in Budapest (public transportation is better).
Flight and train would be under $200 per person.
Another idea is DayTrip.com.
Budapest to Krakow with stops at Oravsky hrad (great castle) and Banská Štiavnica so you get to see a little of Slovakia is about $660 for a private transfer for up to three people, or half the cost of the rental car. They provide the transportation to the stops but the sight seeing is on your own. They are not tour guides.
UBER vs BOLT:
In Budapest, first you probalby will not need either, but if you did, they cost the exact same amount. In Budapest both Uber and Bolt are little more than dispatchers for independent taxi drivers. The Bolt and Uber cars are yellow, very new, in perfect condition, the drivers are licensed taxi drivers and you are charged by a meter in the car just like a taxi, because they are taxis. Nothing wrong with using either. Bolt is more popular for some reason. But I prefer CityTaxi in Budapest. Download their app. It works just like an Uber or Bolt app.
In Vienna both Uber and Bolt work like they do in the US.
In Krakow, I have no idea.