Cape May is our absolute favorite character breakfast (and we have done them all). I love the fun atmosphere and the characters that while fun and lively, isn't some sort of frentic, loud atmosphere with too many screaming kids running around. Its quieter and more relaxed. I also think the food is amazing, they have the best fruit.
If we only do one breakfast these days on our WDW trips, its always this one.
We have always seen Minnie, Goofy, Pluto and either Chip or Dale. All in funky little beach costumes which is sort of cute. The Beach Club is lovely, its easy to get to from Studios if you don't have a car. Take the bus from your resort to MGM, then either walk along the river path (takes about 10-15 minutes) to Beach Club or take the boat (also takes about 10-15 miinutes with the slowness of the boat, the loading and stops you make before you end up at Beach Club). After breakfast its a piece of cake to walk or boat to MGM or Epcot or take Beach Club's bus to another park.