We walked to both, and really enjoyed the walks. As PPs said, Epcot is very close through the International Gateway entrance- 5 minutes away. We found the walk to HS very pleasant, over the bridge past the Swan & Dolphin and along the path adjacent to the Boardwalk. The canal is pretty and we often saw birds, fish, etc. I'd say it was 15 minutes from the BC lobby to the front gate of HS.