There is the Agent P's World Showcase Adventure in Epcot. No reservations are necessary, but they do hand out special devices so I could see them running out. My kids just did this last week and really enjoyed it. It takes about 30-45 minutes (depending on how quickly they figure out the clues) and all takes place in one country but there are multiple scavenger hunts (Mexico, Norway and Great Britain I believe). The day we did it, the system had been down for much of the day but came back up in the evening, so we had not problem getting a device.
There are stations between Great Britain and the International Gateway, by the main walkway from FW to WS on the left, and I believe by Mexico and Norway also. It was quite fun and the kids really enjoyed it. They wanted to do the other hunts but we had an ADR so we didn't have time. It is kind of crazy to see all of these hidden things and have the other guests not even notice them!
There is another group of scavenger hunts in MK and AK but my kids didn't do these so I can speak to those.