I was just in Budapest (yesterday!). Although I did not use Uber, I spoke to a local about it (a knowledgable professional tour guide). She said Uber is definitely there but because it's not regulated at all, locals don't trust it. You run the risk you'd run using any sketchy unlicensed taxi in a place like Budapest—unreasonable extra fees, dangerous drivers, unsafe vehicles, etc. You should never hail a cab from the street, but rather call one of the licensed taxi companies. Any hotel concierge, even if you are just off the street and not staying at that hotel, should help you call a taxi. I found Fötaxi to be the best: clean cars, professional drivers who spoke English very well.