"Well to do and wary"
This area of Madison is beautiful. It's full of trees and parks and at the end of the street is the best beach in Seattle, in my opinion. There are quaint little shops and a Tully's and Starbucks and this delicious little ice cream shop that I can't remember the name of. It's obvious this is a rich or well off neighborhood, because as you ride down Madison the houses become larger and there are more gates and larger gardens. It all makes for a beautiful ride, but is can also be a little uncomfortable if you're not from the area, because you'll find yourself the center of unwanted attention. If that doesn't bother you, then I recommend you go the little ice cream shop, during the summer of course, and walk the two or three blocks to the beach and enjoy the sun and go for a dip!