It's not clear to me why you would choose to stay at Cobalt Coast if you are not diving with them or using their all-inclusive option, and if you like fun and entertainment and trying out restaurants.
CC is a quiet, diver-dedicated resort in West Bay north of Seven Mile Beach. There are a few nice restaurants in the area. Ristorante Pappagallo is north of CC and the Cracked Conch and Macabuca are good places to eat that are south of CC.
We like Cobalt Coast - it's a great venue - but it doesn't sound like what you are looking for, it's mostly for people that like to "eat, sleep, and dive" IMO.
There are loads of restaurants in the 7MB area - what do you like - pricey gourmet restaurants, or more casual places, or local food stands? Or a mix of options?
I have never dived with Living the Dream but they have a good reputation, but you should find out where you will have to meet them to board the boat. If you were staying in the 7MB area then most dive ops will pick you up in a van or on the beach by boat - but since you are staying in a rather remote area, I think you will have to drive to meet them and the traffic can be quite heavy during rush hours. But if they usually leave from the West Bay Dock during that time of year, that should be okay and it won't be a bad drive from CC.
But it would be easier and less time-consuming just to dive with Reef Divers at Cobalt Coast. You could store your gear on the property and their boats will either leave from their dock or they will transport you by van to West Bay Dock.
There are many fine dive ops on GC, it is a very competitive market so a shop wouldn't stay in business very long if they weren't good. There are also good, inexpensive shore dives available, but solo diving is generally not permitted in the Caymans.
When you say that you like fun and entertaining things to do, what do you have in mind? Does that mean eating out and dining and dancing and live music? Or do you mean excursions and nature-based activities? Or all of the above?
You should try to avoid popular venues and the George Town area between 10 am and 3 pm on days when cruise ships are in port, it gets very crowded - and the holidays are one of the busiest times of the year to visit GC.
There's loads of stuff to do on GC, and renting a car is smart, but if you will be drinking while having fun (which is just fine, you'll be on vacation!) then you should stay in a more centrally located area, so that you can easily walk or cab to night spots. Drinking and then driving on the left side of the road, through the traffic and roundabouts, is really not a good idea.
Be sure to reserve your rental car soon, they are in high demand during the holiday season and you might not be able to get one! And's there no uber-type service on GC.
Eating out 3 times a day is very pricey on GC, it's best to stay some place with a kitchen so that you can prepare simple breakfast and lunch meals and then go out for a nice dinner.
If budget is tight and CC had availability at a good price then I can understand that - but maybe we can recommend some place that would work better for your vacation plans - although it will be hard to find availability at this late date.
Take a look at Comfort Suites on 7MB, they offer suites with a microwave and frig and they are on the same side of the street as the beach - they have a small section of 7MB reserved with lawn chairs and amenities that you can access easily by a short path. Daily breakfast is included and you can walk or cab to nearby restaurants and I believe that they offer free parking. Ambassador divers are the group associated with the hotel, but you could make arrangements with LTD or any other op in the area.
The Grand Caymanian (Holiday Inn) might be another option. It is also rather remote but a little more accessible than CC and they offer free shuttles to 7MB and GT - at least during the day - and it might be easier/cheaper to cab there than to CC. I think that breakfast is also included. Dive Tech has an onsite shop and I think that they will provide gear storage and will transport you to their Lighthouse Point facility to shore dive and board their boats.
Sunshine Suites and Sunset House are other properties that come to mind but they are probably already booked up - although they might get a cancellation!
We love the Cayman islands and hope that you have a great time!