I have traveled to the Cayman islands many times. I’ve been to Grand Cayman and Little Cayman. I've stayed at hotels and used independent dive operators and I have stayed at dive resorts with on-site dive operations.
On Grand Cayman, I stayed at hotels on the west end along Seven Mile beach. From these locations, I was able to dive the west end and also the North Wall. The Seven Mile Beach area and the main city, Georgetown, are very developed with large hotels and resorts, restaurants, shops, etc. Cruise ships visit here, so expect everything you would find in most international cruise ship ports. This is also where you will board your liveaboard. This area is an international tourist destination and can be crowded.
If you want to escape the crowds of cruise ship passengers, the East End is the place to go. I have stayed there several times at a dive resort with on-site dive operation. No crowds. Great diving. Wonderful restaurants nearby. Everything most divers want. Don't forget to visit Stingray City before leaving Grand Cayman. Most dive operators will take you there. I thought it might be too “touristy”, but it was a lot of fun.
If you want to go a little more remote, try Little Cayman. This island is very small and there is little to do, other than dive. No worries, the diving is world class on Bloody Bay Wall. I stayed at an all inclusive where the food was exceptional, prepared by a world class chef. Boat rides were no longer than 15 minutes, with most being around 5 minutes. The non-divers with us were content to lounge by the pool, visit the spa, ride bikes, and go for walks. Everything here is very low key and there is a small local population.
You will find the Cayman Islands to be very diverse, from quiet Little Cayman, to bustling Seven Mile Beach on Grand Cayman. From 5 star restaurants to fish frys at the local gas station. From Rolex watches to Caymanite earrings to a shell necklace. This is really a divers paradise.

I have stayed at Compass Point three times. This is a great condo resort. The first and third times with my wife, the second time with a buddy. First time was in an oceanfront 1 bedroom. Second and third time in poolside 1 bedroom. Found the pool side condo to be a little larger. One of us stayed in the bedroom, the other on one of the fold down beds. 2 bathrooms made it perfect for buddies. A hearty breakfast is included with their package. There is a great restaurant on site. Gas grills are available next to their beautiful pool and hot tub. Their east end location is away from all the cruise ship and destination wedding tourists in the Seven Mile Beach area. Many great restaurants in the area. Overall, a great vacation destination.