Compass Point is a good option - Ocean Frontiers is on-site there. If you wanted to drive further there's the Reef or Morritt's but I don't see any advantage to either. Both are Tortuga Divers on-site also. My choice would be Ocean Frontiers though.
There's no shore diving at the Marriott. Red Sail is on-site there but they don't do it anywhere either.
The way shore diving works there at the regular sites is that each one has an on-site operator. They own/have improved the facilities to the water line so you rent tanks from each for that particular dive. Most won't allow "foreign" tanks on property anyway. Technically the water is all public access - getting there without going on private property is the "gotcha".
The three good shore dives north of the Marriott are in the NW Point/West Bay area.
Turtle Reef is a good starting point, SunDivers is on-site there for tank rentals. Rather than describe it - here's the video.
Turtle Reef | Scuba Diving in West Bay | iDive Cayman - it's IMO one of the best shore dives.
Lighthouse Point and Cobalt Coast are similar except since CC is around the point on the north side, you have to option to go out on the deep North Wall there.
Divetech has a shop on either location, the one at Cobalt Coast used to provide one-way drops (probably still does) out on the wall so you can dive it then swim back in. They also run the West Bay Express once a week - an escorted scooter dive between their facilities.
Moving the other direction from the Marriott - Wall to Wall has a location at Lobster Post Dive center in north Georgetown. If you dive with them they give you a free tank to be used that afternoon at Cheeseburger Reef off their dock. It's not the best of Cayman shore diving but it is a reef. From the Marriott - about 2 miles south.
Next is Eden Rock/Devils Grotto - a series of shallow coral swim-thru's.
Eden Rock Dive is on-site - it's also one of 2-3 locations on Cayman that will let you rent tanks for off-site diving - the other being Divers Supply and a 3rd I forget.
Eden Rock is 500' south of the cruise port so that hasn't done it much good over the decades. Also there can be up to 10K cruisers in port on a normal day (4-5 ships) so it's pretty congested till they leave around 4PM. If you start gearing up around 3:30 there you can do an hour dive b4 they close at 5PM - most of the cruisers will be gone. It's all in the 40' range. The Grotto is pretty bleak but a lot of swim-thru's. It's fantastic in summer when the Silversides invade - in April it's you and a few forlorn Tarpon.
Slightly south of there is Don Fosters - they dive the south side of Devils Grotto.
1/2 mile or so farther south is Sunset House - the AI dive resort. There's a small landing craft wreck there, the famous Mermaid (Amphitrite) statue in 55' and at the right time, the tourist sub will go thru there also. I like spending the afternoon there - My Bar is a divers bar with good food, you can watch the diving going on out front and there's two access points to the reef - the dock or the saltwater pool (open to the ocean) 50' north. The Cathy Church Photo Gallery/Shop there is also worth a look - nice lady who'll sign a print you buy if she's around. And talk diving with you for the next hour...lol.
Sunset House - George Town - Cayman Islands
A little south past that is Smith's Cove - a shallow beach dive. No facilities so bring tanks rented from Eden Rock to dive it - they have a 24 hr. rental period.
That's pretty much all the accessible shore dives on GC. Some people dive Cemetery Beach on the north end of SMB but it's pretty shallow - you're likely to see good snorkelers at the "dive" site. You'd have to bring tanks for it also.
I don't think Ambassador or Living the Dream provides tank rentals. Neither do any of the boat based operators - some run their operations via website/phone and meet at the marina so tanks are just for their boat dives. Or in the case of Ambassador they have an office at Comfort Suites but there's no dive there - they keep their boats at one or two nearby marinas.