Budapest: Buda Hills
Take the M1 metro (runs just below street level, uses smaller trains to fit the special short tunnel) from Oktagon to Deák Ferenc Tér. Change to the M2 line (bigger trains, different tunnels, linked by escalators deep underground) to go under the Danube to Moszkva tér (Moscow Square) and catch either the 59 or 61 (old-style) tram for two stops. (Note: Loney Planet incorrectly suggests tram 18 or 56 for this leg.)
You’ll see the circular Hotel Budapest. Across the street, through the shrubbery is a footpath to the Cog Railway terminus (built in 1874.)
Ride the Cog up to Széchenyi-hegy, walk south for two minutes to the Children’s Railway (built in 1951 by Soviet Scouts.) Get off at the 4th stop, János-hegy, and hike uphill. There is a little playground. Hike uphill some more to the highest point of Budapest, and climb the 101 steps of Erzsébet-kilátó (Elizabeth Lookout, built in 1908).
Go back downhill a little way and take a chairlift down the mountain. Children under 3 ride free. Walk a little way down the road to catch a bus back to Moszkva tér. Switch to (modern, air conditioned!) tram 4 or 6. Our hotel is just one stop past Oktagon on this tram line.
Simple.
