I have just returned from Budapest and had a great time.
I have to say that I was cautious prior to travelling there following the reports I had read about the city. However I have to say that in my experience these were unfounded.
I found the city to extremely safe and I had no problems walking around day or night. In fact I found it to be a relatively quiet city.
Taxi from the airport (Fo Taxi), ordered from the booth outside arrivals took around 30 minutes to the city centre and cost around £20. The price seemed fair, the car was comfortable and the driver polite and friendly. No complaints here.
The only note of caution I would mention is that I was approached several times by pairs of young girls on Vaci Utca and the square at the end of it (sorry can’t remember it’s name) asking for directions to certain bars. Mindful of the reported scams luring you to dodgy bars I politely declined and walked on without further incident. If those girls were genuinely lost then I apologise for not helping them.
Budapest is a genuinely beautiful city and seeing the castle and chain bridge lit up at night was spectacular. The funicular ride up to the castle is a must as is the parliament while the Jewish shoe memorial on the banks of the Danube is very simple yet effective.
Didn’t have time to visit Hero’s Square which I would have liked to have done. Still it gives me an excuse to return to Budapest in the future.
One final piece of advice is that it was really cold there when I visited (January) at -5oC so wrap up warm.