With all your restrictions, I don't see anything except an AI on Curacao working for you. I don't think you can get a Sunday flight from your area to Bonaire, you have to fly direct on Saturday morning out of Newark or Houston via Continental or do a long layover in San Juan to catch AA to Bonaire Saturday/Sunday evening. As I recall, we did a Friday night red-eye into San Juan to catch the Sat. night AA flight to Bonaire.
So if you can change your schedule, Bonaire's a good option.
Capt' Don's Habitat would give you the most different diving immediately offshore, they sit on two dive sites - Cliff and LaMachaca - although they sort of blend together. One part of Cliff is a mini-wall. Also near that area is Buddy Dive or SandDollar/Den Laman Condos and Bari Reef. Den Laman is pretty new.
Or you could go south and stay at the Plaza, but there's only one site there and it's a pretty good walk to town. Nice resort though and close to the airport. Another option would be the Divi Flamingo. You can walk to downtown from there.
Renting a car on Bonaire would open up to a whole lot more possibilities.
Although frankly (and dvrliz1 will disagree I hope), in my opinion Bonaire is not somewhere I'd go for my honeymoon, the whole island is geared around diving. We didn't find much else to do there except some sightseeing.
Freeport is out, the shorediving in non-existent. As is Nassau mostly. There is a few shoredive spots but they're pretty spaced out so a car would be required. Most of the diving there is boat-diving with Stuart Cove.
You might also consider Sunset House on Grand Cayman. It's a short flight from Miami, the shorediving is interesting enough to do more than once. Sunset House has a full restaurant, outdoor bar/sandwich place and is about a mile from downtown Georgetown. It's a dive resort though so the amenities, while nice are plain. But they refurbished everything after the hurricane so its probably nicer now. There's a wreck, the famous Mermaid and a lot of shallow reef structures there. With a longer swim you can get out to some sand chutes that drop off deep.
And they'll take you in a van to a boat for a short ride out to Stingray City, which is in the protected North Sound so pretty much flat calm and only 15' of water. And it's a lot of fun. If you're photographers, the Cathy Church U/W school is onsite also.
A short/cheap cab ride would let you also dive Eden Rock/Devils Grottto and two other dive sites in the GT area. All provide tanks onsite and have easy stair entries. Most of the cabs are mini-vans so gear isn't a problem.
Turtle Reef up north is imho the
best shoredive on Cayman, it's about a 20-30min. cab ride from Sunset House. Divetech has a facility there and rents everything including scooters. There's a mini-wall 50' offshore that's full of life and would easily take several dives to see it all and you can also go out the North Wall from there, but it's a healthy swim. (hence the scooter rentals) You're also likely to see Turtles there as the Turtle Farm is right next door. We saw lots of Tarpon in the shadows and a school of Eagle Rays flew over one time.
Downside with Cayman is that you might run into a Hurricane in September. And food is wicked expensive - actually most things there are. As Curacao or Bonaire are out of the hurricane belt they might be a better option.
www.shorediving.com for other options.