To Magic Kingdom: bus (We stayed at the BWI in December for the first time and having stayed at the Grand Floridian or Polynesian all of my life, I was a little worried about the bus. I shouoldn't have been. We never waited more than 5 minutes for a bus either at the resort or the park.)
To Epcot: walkway (very short and you enter through World Showcase) or boat
To MGM: walkway (probably a little under a mile, but a very pleasant walk) or boat
To Animal Kingdom: bus (once again, very short waits at both stops)
To Downtown Disney: bus (direct service all day)
As for the boats and buses, if the BoardWalk isn't the first stop, get off at any of the other resorts (Swan, Dolphin, Beach and Yacht Club) and walk. It's a very short distance from any of the above mentioned resorts.
You can also take taxis to any location in WDW. We didn't have to use taxis nearly as much at the BWI as at the GF. And even when we did, it was personal preference, not a long wait at the bus stop. Have a wonderful trip!