Both Dania Beach and Lauderdale by the Sea are nice beach dive sites.
Here's my brief thoughts: LBTS is an easier swim to the reef. There are little restaurants in the area that are nice to wander up to before or after you dive but the parking is a pain. Unless you arrive early, you'll be lugging your gear a long distance. Additionally, the showers are located in convenient areas for washing gear, but there aren't many public restrooms.
Dania's reef feels like it is a bit further out to me. I have not been to Dania recently, but last time I was, the restaurant by the pier was closed. Parking is unlimited plus you have some restrooms to use. Dania also has showers, but the water pressure is lower than LBTS. Dania also has Erojacks (sp?) that are well north of the pier: I've not dove them, but I hear they are interesting. Youtube videos I've seen are pretty cool.
Both reefs are very nice and beautiful, but I like Dania's slightly better: there's more relief to it. But again, both sites are great to dive if marine conditions are decent.
Gold Coast Scuba's meetup group does dives at both locations; you can join the club and then pick a day to go to the beach with your family when other divers will also be there.
You can search Shorediving.com for additional information.