Unless you are sticking to boat dives where they pick you up, to get the most out of the weekend you might consider a car. I don't think cabs or public transportation are a practical way to do shore dives, even if they'll let you. I've repeatedly seen other people do the same thing, start with no plans to get a car and want one by the second day. (I think we did this ourselves first time there...)
If you want to do a night shore dive someplace, check how they work things as you likely need to plan ahead. I know when Dive Tech was at Turtle Reef they would be closed and locked up at night (and the rinse tanks would be empty with water off.) If you were diving with them you just had to plan ahead and they would stick your name on some tanks and leave them outside. Sundivers may do the same, don't know. If you were staying at Sunset House you would have to get tanks before they closed and stick them in your locker. Don't know how it would work if you weren't staying there. Some places may offer guided shore dives or occasionally boat dives at night which avoids the "not open" problem but you'd still need to prearrange - and it seems Fri/Sat night would be the least likely nights they'd do them, as most people are either just arriving or departing the next morning.