I'm in Tuscaloosa currently, but I'm originally from Huntsville. Brahan might be the most populated course due to its beginner friendly nature, but most of the locals that have been playing a while play all over the place. My favorite of the Huntsville courses has to be Indian Creek, but really they all offer a different challenge.
Brahan was where I learned to play. It's a reasonably short course, but whoever designed it definitely did the most with what they had. Slight elevation changes, good tee signs, concrete tees, so on and so forth. Always a lot of people here when the weather is nice.
Mastin Lake is probably the least populated of all of the courses. It offers some nice challenges and has continued to improve over the years with the increased interest in Disc in the area.
Monte Sano is a lot of fun. It's part of the State Park up there. From experience, unless you hit the fairway every throw, don't use an orange disc in the fall (blends in with the fallen leaves). It's very nice up there though.
Dublin in Madison shouldn't really be bothered with unless you're not afraid of hitting children and you really need some putting practice. The holes are extremely short and it's far to populated around the course unless its raining.
UAH is excellent. It's the past site of a couple of Worlds. There are a few holes that you can really air it out on (RHBH and LHBH). As far as technical shots, there aren't many. Water, however, does come into play.
Indian Creek is the newest and in my opinion best course in Huntsville, the only issue being that when it rains, there is some problem with mud. It uses the natural surroundings to create a fun and challenging course that doesn't really get repetitive. Long shots, tight shots, up hills, down hills, dog legs, blind shots, elevated baskets, and more. I fully expect some high caliber tournaments to be gracing the course in days to come. If you're looking for a home course, I'd suggest ICDGC.
Like Rip said, the rocket city chain gang is a group of nice people that are increasingly active. When I was last up there, they were still hosting weekly doubles Tournaments.
One of the Disc Golf Hall of Fame Members (and I believe co-founder) Lavone Wolfe lives in Huntsville too. I believe he sells discs and accessories out of a store on University. Also, Greek Etc. on Jordon sells some discs.
I know this isn't exactly what you were looking for, but since I don't live up there anymore, it's the best I can do! If you ever make it down toward Tuscaloosa, let me know. I'll take you around Bowers.