In Budapest go and climb Gellert hill behind the Gellert hotel; the views are great. Then walk down and have a swim in the truly amazing baths at the back of the hotel; incredible 1901 baroque architecture and an inside pool, several outside pools and a wave machine. Lying in a hot pool under the autumn trees will be a nice way to relax tired muscles after the walk. Watch out for the Hungarian attendants walking around with weird rubber hoses and apparatuses and going into cubicles occupied by fat Germans…
Then finish with tea or a beer on the Gellert hotel terrace. If you’ve time, stroll across the bridge and turn immediately right into the beautiful covered market (designed by Gustav Eiffel I think) the after you’ve marvelled at the fresh produce, climb the stairs to the inside terrace and have an evening aperitif of the special liquor they brew from grape skins second time around.
Also take the time to have a look inside the lobby of the Four Seasons Gresham hotel on the opposite bank from Gellert; it was built by the British Gresham insurance company in 1906, had a fascinating history and was restored as an hotel a few years ago. Mrs Gti and I explored it when it was a blackened, virtually derelict shell full of pigeons.
Great city, Budapest.