I doubt if any of those day boats in Belize City would make it out to the barrier, more than likely they’ll take you to the reefs around Lighthouse which is still good diving. You can use ScubaEarth up top to zoom in on Belize City to review some of the sites on the off chance the crew ask where you want to dive.
I stayed in Belize City a few days (don’t!) but did my diving from a liveaboard so I can’t reccomend any shops.