My son was crawling when we went in the fall.
We let him crawl pretty much anywhere there weren't alot of people. We didn't use any knee pads, but he would do kind of an elephant walk if the ground bothered him. Actually quite cute! He was cruising too and enjoyed pushing his stroller around (while I steered/controlled it). A few good spots that I remember:
Epcot:
Innoventions - find a quite corner
Test Track - the GM Display area
The Land - the restaurant sitting area at non-meal times
China - the waiting area for the movie
America - the waiting area for American Adventure
France - back behind the perfume store (waterside)
Magic Kingdom:
Poohs Playground - watch out for big kids though, find a quiet corner and have adults block off as best as possible or go when quiet
Tomorrowland - by the closed Galaxy Theater by Buzz
Disney-MGM Studios:
Animation Building - there is a interactive area at the end of the "tour" or you can go in through the Art Store. Wide open area, not too much traffic, lots of carpet.
Exit area of Sounds Dangerous - lots of carpet, just watch for the show dump
Honey I Shrunk...Playground - Toddler area, again watch for big kids though
Walts One Man's Dream - Lots of crawl space here, just watch for other guests coming through
Animal Kingdom:
The Boneyard/Dig Area - again watch for big kids
Animal Trail Behind Tree of Life
And if your willing to let your little one get wet, the DS loved the sprinkler areas. Just stake out a spot and have the adults watch out for the bigger kids. By DS & DNiece had a ball at one lily pad at Donalds Boat at the MK. We were at one that was on the edge of the playground and my husband sort of stood between it and the rest of the area to ward off others.
Just look for those off the path places. It's actually amazing how there can be a quiet spot just yards away from the hustle and bustle of the main pathways.