Search the posts on SB and you will see shore dives sites described for Turtle Reef, Lighthouse Point, Eden Rock/Grotto and reviewed. I have dove all three many times and enjoy all three. Turtle Reef is my favorite for ease, great dive op and great place to eat/drink after your dive. Eden Rock/Grotto is best dived when no cruise ships are in port, weekends are best.
What part of the island are you planning on staying at? On 7mb, west side all this sites easily reached by car. If you are staying on the East End, not so much. There are dive ops who you can schedule one tank boat dives. Also, if staying and diving on 7MB, west side the boat rides are typically short and the waters calm. My wife is very prone to sea sickness and we usually only do one tank short boat trips. We did a dive on a small six pack that took us at for a two tank and we had no problem as the they picked us up right on the beach we were staying at, 2 min trip to site one right of the beach, dive, SI and 2 min ride to the next site. The boat rides are not all this short but it gives you an idea.