Boat dives from Sunset House tend to stay along the west/south sides due to the distance. What's kind of odd about their site list is that North and East sites are listed first, I'd be very surprised if they do any of those on a regular 2-tank. Almost nobody does the East side except on special excursions.
The Kittiwake as mentioned might be a good option, anyone OW can dive the 1st three decks. Stingray City can also be a lot of fun one afternoon, from SH they'll van shuttle you over to their boat on the sound. They keep one at the north pier for that.
If they still do it, once everyone is on the boat they'll ask for suggestions. Some off that list you could ask about:
south
Japanese Gardens
Blackie's Hole - we liked this dive.
Eagle Ray Rock (not Pass)
west
Killer Puffer
Aquarium
Knife
Trinity Caves (IIRC deeper than they list)
Orange Canyon (IIRC deeper than they list)
Bonnie's Arch
Big Tunnels (listed at 55' but the Tunnel is 90+) Staying above it you're mostly in blue water.
I think their listing is showing mooring depth and not dive depth. Most of the sites could be up to 100' for the 1st dive. Many have a shallower option but some don't.
Turtle Reef would be a good 1st shore dive. It's a bit of a drive from SH but it's shallow, has an easy entry and the mini-wall is 40yds. offshore. And bottoms out at around 50-70'. The wall is just covered with stuff, as the name indicates there's always turtles there and if you go south there'll be a hundred+ Tarpon hovering in the shadows pretty shallow. Nearby both Lighthouse Point and Cobalt Coast are also shore options. If you don't have a car, Andy's Rental will pick you up. SH probably has arrangements also.
If the Silversides are still in at Devil's Grotto in town (maybe another month) that's an excellent interesting shallow dive. Not so much if they're not - it's pretty featureless with a few wistful Tarpon still hoping. It's also 100 yds from the cruise port so plan accordingly. You'll see the ships from Sunset House. it's a cheap cab ride. You can also dive Eden Rock at the same location. Eden Rock Dive has tanks on-site - Sunset actually won't let you remove them from their property.
We also had a very pleasant afternoon at Sunset House. Surface swam out to the Nicholson ball then dropped and drifted back over the Mermaid and ended up in the shallows to the north of the Saltwater Pool. We must've been near the photo school practice area because the fish were super friendly. My Bar is great after.