Besides hotbars and gear sets that were already mentioned, your macros, HUD layout, and Triple Triad decks are also stored locally on each machine. (TT cards themselves are kept server-side and available from any platform, but your choices of which groups to use as a five-card deck aren't.) I think all the options under "Character Settings" are local as well, but I'm not positive on that part.

Gear sets seem to be the most annoying though (at least to me), since they tend to change the most often. I really wish SE stored our gear sets on the servers with the rest of our character info, so we could access them from any platform.