Grand Cayman also has an excellent and inexpensive public bus system that is easy to use. The buses are more like extended mini vans, and the drivers will cram as many people as will fit into them, but they run up and down the main street past 7-mile beach all day. There are numerous beach access sidewalks located between most of the hotels. 7-mile beach is fantastic; you won't be disappointed.
The bus station is a short 2-3 block walk from the area where the tenders dock- just ask directions or find it on a map. It's not really a station; more like a bus stop on the corner, but they'll take you to all the popular spots.