As already noted, the Beach Club is the closest Epcot resort to the International Gateway. It's at most a 5 minute walk. In June the BC and YC had their own bus while the Boardwalk shared with the Swan and Dolphin. Even the furthest resorts (Swan/Dolphin) are only maybe 10-15 minutes tops to the IG of Epcot.
If you go to one of the Epcot resorts you will need to enter the resort and walk through the lobby to exit at the boardwalk/lake side. From the BC/YC you would then turn left to get to Epcot. From the BWI turn right. Swan/Dolphin you should walk towards the Yacht Club (straight ahead) and continue on from there.