August should be fine. While Roatan could be hit with a hurricane, it is below the normal hurricane routes so the chances are slim. The rainy season doesn't start until late September.
As for places to stay and dive shops? Where to start? It depends on just what you're looking for. There are dive shops all over Roatan with places to stay either on site or nearby. I've only dived on the west end of the island, either at Anthony's Key, which is an (almost) all-inclusive resort or in West End. If you want an all-inclusive, there are several to choose from...Anthony's Key, Coco View, Mayan Princess, and Turquoise Bay, just to name a few. All are excellent choices. If you want something that is not as costly, I have stayed at Mame Tree and Hotel Posada Arco Iris. Both are economical but somewhat on the rustic side. Mame Tree does have some efficiency rooms that are nice. Both of these are within a very short walk of dive shops. In fact, you can't throw a rock in West End without hitting a dive shop.
There are a few dive shops that also have Stay and Dive packages. One is Coconut Tree Divers at the north end of West End. I've not stayed there but I have dived with them. We were happy with the diving there and would dive with them again. Another one is Splash Inn Dive resort a little further south but still in West End. It has its own restaurant which we have eaten at several times. Breakfast is included if you stay there. If I didn't want to go to a AI resort, I'd strongly consider them. I have talked to people staying there and they seemed quite happy with them. A couple of other dive shops that I have not dived with but have excellent reputations are Sun Divers and Roatan Divers.
Good luck with choosing a place to stay and/or dive. The choices are many.