They don't always have it open during the day at DTD, ymmv so be prepared, especially if your going just for the wrap. Go go early evening and it should not be to bad but it can take at least 15 minutes per person, more if a child has long hair.
It is also offered at all the resort pools but our favorite is on the Boardwalk. Lots to do and see while we wait and they seem to do a terrific job. My 8yo had one done the day after Christmas and it just started to slide out on Monday of this week. I was able to cut it in time to save it and attach to a hair clip so she can still wear it. The cost is 1.50 per inch + beads, the beads vary greatly in price and can significantly add to the cost.
MK offers it at the POC shop and I have seen it at AK but personally I didn't want to waste my park time on a hair wrap. We save this for a non park day too!
Have fun.
TJ