That's a very limited amount of walking, and I think it would be tough to find a large city that works without heavy reliance on taxis (which might be my plan). The most popular destinations tend to be the historic ones, and old cities were often built on hills, or at least their oldest monuments were. I guess a key factor is how important it is to go somewhere with a lot of specific sights to see, as opposed to areas where it's more about the beauty of the total environment (Berlin vs. Switzerland, for example).
I'd think about areas that are flat, cities that are small (without lots of spread-out sites), and highly scenic areas where local train, bus or boat trips are sights in themselves, with no walking required. You can stay in one of the flat valley towns in the Alto Adige (Bressanone, Bolzano) and take gorgeous daily trips into the Dolomites, for example. I sometimes hop on a bus, ride to the end of the line, and immediately return. Virtually no walking at all.
Also consider that countries like Italy and Spain have a lot churches scattered throughout their historic districts. Many of them are open throughout the day and have no entry fees. They are good resting spots.
Trams usually sit lower to the ground than buses and are thus easier to get on. They are better for the mobility-challenged than subways, whose stations can be rather widely scattered and/or require a lot of walking within the stations.