I'm not positive, but I think Disney parking is about $8 per day (I'm sure one of the S. Cal residents on this board can answer better).
I also stayed at the Hyatt about a year and a half ago, and we relied on the shuttle, and also thought it was great. We never waited more than 10 minutes, and the stops we made were very short. Personally, unless the shuttles are really packed, it probably saves time over parking in the Disney parking structure and waiting for the tram to take you to the parks.