You could walk to French Cay from Barefoot Cay. It's the only south side resort close enough, Cocoview/Fantasy Island are about 15mins. drive away. We dove with Barefoot Divers and if I ever return to Roatan they'd be high on my list to stay with. IDK if you can do it within your budget unless you get one of the lofts in the main building on the shore (non Cay) side.
Any sort of nightlife will be in the West End though. There's a lot of rooms/apts./small cabins that would be well within your budget in and walking distance to town. Cocolobo looked really nice, >10min. walk to the West End from there. Closer in town, Posada Arco Iris is right across the street from the beach. So is Coconut Tree cabins further down. I'd stay at any of them from a safety/convenience standpoint. Woody's Market is between Posada and CT and there's another small market at CT in the main building. Some friends stayed at CT cabins, they're older but clean. The West End was mostly quiet all week after about 10PM except for things pickup a little closer to Friday - esp for most Sat-Sat divers since it's their last night.
Lots of good info here:
http://www.bayislandsdiver.com/
We did 4 dives/day with Coconut Tree but my group was almost all their business that week - they seemed to indicate that 3/day was more typical depending on customers. They also do a couple of night dives during the week. Good people, good crew, ask Gay in the shop for anything you need, she knows everybody.
Reef House Resort is even further removed from everything than any of the others.
Anthony's Key is nice but you dive there, eat there etc. It's on it's own private oceanfront so is removed from the main road - although realistically there isn't much along the road until you get into the West End - about a 5-10 min. cab ride away.
Cabs are cheap and plentiful in the West End if you want to go somewhere else. The taxi stand is across the street from Coconut Tree - unless it was very early in the morning there were always cabs waiting. It's about a $5-6 ride to AKR.
One other place to consider is Luna Beach Resort. It's on the far west of the West End so would be a long walk to "downtown" but they have a water taxi. Also I believe there's a shore dive there.
One tip: When you get off the plane, get in the right lane for immigration. (You'll see why once you round the corner...)