Several good dive sites above, but you are asking a question that is larger than this.
You have to understand one basic fact about Roatan. Because of the shape of the island (17x3 miles, give or take) and the lack of roads- plus once you get away from West End... the dive operators get pretty spread out... you can not access more than just a few localized dive sites while diving with any specific dive services provider. (contrary to what a few of them would have you believe)
If you want to experience the different zones of diving, you have to go with the local provider in that area.
It roughly breaks down into 4 zones.
The most heavily served area is the West End and it's near North side environs. Day-dive ops abound, plus AKR as a major player in the AI market. Most of the dive ops in that area (including West Bay) trumpet that they also will show you some South side dive spots, but largely they are only referring to the vaunted and highly over-rated Mary's Place. The general character of the diving in the West/North is affected by the Marina Reserva so you will easily see larger Crabs, Lobster and some of the mid range predators like Barracuda, etc. In the Summer months the seas are flat, but unfortunately there isn't much breeze and the bugs can get bad while on land. The diving is comparatively deeper (as are the wrecks are battered and @ 100') than other zones, the reefs are more stark (due to this being the part of the island that takes the brunt of storms) and has some cool architecture or shapes. The muck-dive in the tidal basin at AKR is arguably the best night dive on the island. Very close to (or within) the party scene.
The next most served area is the South Side between French Harbour and First Bight. This is an "all AI" zone, pretty much~ no day-dive ops. You can hook up on a daily with Barefoot Key (BFK), but otherwise for strictly AI's there is CCV (CocoView). Fantasy Island may or may not be viable this week, and a new place, Media Luna is a "resort that offers some diving". The zone of diving they serve is absolutely unique in the Caribbean. It provides very shallow (5~90fsw) vertical walls that are Sunlit all day long. A lot of life hides in this lush colorful wall structure, unfortunately invisible to newer divers. This is not an area for those still fascinated by Caribbean Lobsters and Harbour Crabs. The walls are fairly repetitive in shape, not a lot of variations in physical features- so that is another negative for some newer divers. The two extremely shallow (60') wrecks are a huge draw- they are intact. This area also has the Shark Dive and Mary's Place, but those are two dive sites that any visitor to Roatan can get to. It is the spot in the Caribbean for macro photographers. There is usually a 2' running sea, so pick your dive boats with care. Fewer bugs and very limited impact by storms. The best shore dive on Roatan- it features an intact 140' ship, upright in 35-65fsw- it's also a great night dive.
The two remaining zones are located towards the Eastern end of the island. The area on the North is not well served by dive operations, largely because there isn't a whole lot to see of interest. (exceptions noted below) The only service there is from Turquiose Bay which offers diving as an afterthought, but one of the single best DMs on the island works there, Osman Gomez. He is a superb naturalist guide. The better dive-ops (like AKR) can get you from the far West of the North side and get you to some very interesting dive sites like Dolphin Den and others.
Also in the Eastern end but this time on the South side is an interesting area that was mentioned earlier as having the dive site "Calvin's Crack". This area is served by only one viable dive-op, and AI called Reef House Resort (RHR). It is very close to Calvin, also often accessed by CCV. The reef structure here is a mix of vertical and sloping, lots of very cool stuff to see, the weather can be a bit harsh (this is the side the wind usually comes from).
I was fortunate enough to have an associate with a boat and a lot of time, so many years ago, he dragged me (literally) around the entire "island(s) of Roatan". (Helena and Morat, too).
The "best dive sites"?
It really depends upon what you are ready to see. If you have great buoyancy skills and are a really good observer, the South side offers incredible macro opportunities found nowhere else in the Caribbean. <- that's a period
But, if you are a new diver, you will likely walk away from the South side thinking it is devoid of life.
If you are kind-of new at this diving thing, I would point you towards the West End/near North areas. Lots of bigger stuff to see, you get to go deep, and one of the biggest concerns of most travelers is well met... where are the bars?
