Madeira has a temperate climate all year round. We went there in early November, and it was in the 70s most days.
Funchal is the main resort, with many hotels to choose from, but as already mentioned, it IS quite hilly. I can't comment on bus services, but there are lots of taxis, which are quite reasonable. Driving isn't a good idea - we hired a car for a few days, but the drivers are a bit manic, and the mountain roads can be a bit nerve-wracking due to rocky outcrops.
There is a beautiful Botanic garden nearby, which, due to the climate is always nice to visit.
Congratulations on your Golden anniversary!