Grand Cayman is small enough to feel safe, yet there is a nice variety of things to do. Tourism is moderate and with significant development underway. I'm a beach girl so Seven Mile Beach is my favorite, and consistently ranked as one of the most beaches in the world.
For this trip, I chose the Grand Cayman Marriott Hotel. The Marriott's accomodations were first-rate with excellent room and guest services (see pictures). This is one of the few large-chain hotels at which I've stayed in the Caribbean that actually FELT like the Caribbean (at least a 'lite' version). The Marriott's food was so-so. There's local fare within walking distance though so you may want to venture out for snacks during the day and more formal dining in the evening.
A friend of mine has vacationed at The Westin Hotel on Grand Cayman and she loved it. Indeed, the The Westin Hotel offers excellent accomodations and their food is GREAT. I had lunch at The Westin Hotel and found the menu to have the usual continental items along with delicious local fare. The beaches at the Westin are smooth with calmer waves and tides during the day than the Marriott.
Needless to say, resort properties are abound on Grand Cayman so you have many options to choose from.
Want to learn more about the island before your trip, visit the Caymans Tourism Site.