Lake Roberts is one of my favorite places to visit! Do yourself a favor and don't go to a cabin. One of the best ways to experience this area is by camping. I've been coming for years and always have such a wonderful time!
The Upper End and Mesa campground are first come first served basis. Mesa has hookups for RVs and running water at almost every campsite. The Upper End is only dry camping however there are water faucets at both ends of the campground near the restrooms. I found the campground and the restrooms to be really clean. Well behaved dogs are welcome and of course there is fishing. One year we caught 21 fish in 2 hours!!
Don't forget to take some time to visit the Gila Cliff Dwellings and the hot springs!