We flew independently to Budapest and easily got a taxi outside the airport terminal doors to the Corinthia Hotel. The taxi rate is fixed by zone and I think we paid about 20 Euros (Forints not necessary) for the approximate 20 minute drive to the city centre (Pest side).
The Corinthia had a room for us early in the morning, was beautiful and comfortable but we would have preferred staying closer to the river and main shopping area--maybe the Marriott, Sofitel or Intercontinental.
I concur with the comments posted previously by Charlotte T. and Adjohn so I will just make some additional comments:
Although this is an older ship, it is in mostly beautiful condition and is easy to navigate on the short flights of centrally located stairs
-There is a conveniently located launderette with 2 washers and dryers. Detergent and use are provided at no additional cost
-Uniworld gives cruisers stainless steel water bottles and replaces fresh water daily
-There is one large umbrella in every cabin and additional available when exiting the ship
-There is a blue night light that remains on in the bathroom ceiling
-Wifi was only available in the lounges. It was slow and not available when going through the 67 locks. Bringing a newer device will make connection faster
-Since we don't know if we will get back to that part of Europe again, we took all the optional excursions and they were excellent. Most were in the afternoon, after lunch on the ship. The cost isn't posted (but it's reasonable) until you board but you can sign up for them a day or two ahead or all at once after the CD talks about what's offered at the initial welcome meeting
-The dining staff offered 3 nights of dining topside in a glass enclosed room where there was a fixed menu and steaks were grilled
-Fellow cruisers were Americans, Australians, New Zealanders and Canadians--a congenial group of 103 passengers of ages late 50's to 80's
-Disembarkation was well organized and executed. Passengers could select when they wanted to leave the ship and transport was arranged by the staff. We stayed additional time in Amsterdam and the staff had a taxi waiting to take us to our hotel when we specified. Passengers must vacate cabins by 8:30 AM but are welcome to stay on in the lounge through a light lunch time there, even as new passengers are boarding.
We highly recommend Uniworld and we really enjoyed river cruising.