I agree that Blackbeards is the least expensive option, especially if you want to stay close to $1000, but if you are looking for better accommodations, better diving, and more dives per week, then I think that the suggestions from
@Damselfish were good ones.
If you are traveling alone then you need to be willing to share a cabin with a same sex diver to get the best rate on many liveaboards (but if the boat doesn't sell out they may let you have the cabin to yourself at the cheaper double occupancy rate.) That's not an issue on the dormitory style Blackbeards liveaboards.
Below are some current specials being offered by Explorer and Aggressor. They are more expensive than Blackbeards but better accommodations and better diving IMO (and more dives!) but the airfare may be higher.
Out of these 4 I think that the T&C Explorer offers the best easy access diving. Fabulous walls, lots of sea life and sharks and rays on just about every dive. Also, a liveaboard is the best way to get the best diving in the T&Cs but they are only available in the last 3 quarters of the year because the LOB T&C boats offer whale watching trips early in the year.
The Saba/St. Martin/St. Kitts Explorer is the cheapest and it is very good diving and you will get to visit 3 different Caribbean islands so that's great. I don't think that you would be disappointed.
In my experience, the Red Sea has the best diving among these destinations, but it isn't easy to get there and the airfare may be pricey, and US citizens might not be comfortable traveling to Egypt during these troubled times. On the other hand, it is a wonderful opportunity to visit a fascinating country with spectacular diving - and you may not get another chance for a long, long time.
Roatan is my least favorite out of these 4 options, but it still good diving and it does give you the opportunity to dive Roatan, Utila, and other sites (I've only dived Roatan). Also, this special introductory price is likely to increase soon, so it may be a good idea to take advantage while it is available.
If you are willing to consider a land-based trip, Anthony's Key Resort on Roatan is again offering their "buy one get one free" promotion - which I think is the same as "you don't have to pay a single supplement if you are traveling alone" promotion, see the link below.
The prices start near $1000 and include diving and all meals, but be aware that there will be a 19% tax on top of the resort price, also some of the rooms don't include air conditioning and you may have to pay a bit more to keep cool. Airfare to Roatan can be pricey but Cayman Airways recently started offering flights to Roatan so that may help the cause.
Buy One Get One Free | Anthony's Key Resort | Roatan | Honduras
Just food for thought, I hope you find a great, economical, dive vacation!