The Boardwalk to Epcot is approximately a 5-7 minute walk. Very close. The Beach Club is a bit closer, and is probably only a 3-4 minute walk.
The Boardwalk to MGM is an 11 minute walk.* The Beach Club is a little bit farther, and is probably a 15-16 minute walk.
* 11 minutes sounds weird, but there's an interesting -- to me, anyway -- story behind it. A few years back, my buddy and I had just missed the boat to go back to the Boardwalk from MGM. We didn't feel like waiting and asked a CM how long of a walk it was back to the Boardwalk. The CM responded that it was 11 minutes. The bit of precision kind of surprised us, and we had a good laugh ("it's 11 minutes, huh? Not 10? Not 12? 11?".... "Yep, 11 minutes."). So, off we walked (with stop watch started) and, when we got to the Boardwalk, lo and behold, 11 minutes. Granted, I do walk at a faster than average pace, but I was by no means speed walking or attempting to walk faster in anyway... just a normal walking pace for me. The time might be a bit longer for someone with a stroller, but it's still a fairly easy walk. If you leave to walk there at the same time the boat does, due to the stops the boat makes, you'll more than likely beat it to MGM.