Captain Marvin's offers island tours which include the turtle farm (on your own, turtle farm admission is $30, we paid $30 for tour). The tour will drop you off at the beach or the tender area--your choice. They also offer snorkeling tours which are great fun.
Boatswain's (google them) has an assortment of packages available. They are where the turtle farm is, but there are many other activities available. Easy on your own.
If you just want a beach day, all beaches are free at Grand Cayman. There are brown signs indicating public walkways to get to the beaches. THere is a public shuttle or cab transportation available to the main beaches (7 Mile Beach and Sea Grape Beach).
Your real issue is the 2 year old....there's not much that will thrill him all day long.