I am staying at Cobalt Coast because I have a "timeshare" type of a thing and that is where there happened to be availability on the dates I could go
Same for me about how I stay on GC, although we did pay for a week at Ocean Frontiers once, because of availability of dates. It sounds as if you've done your research. Diving with Reef Divers at CC would not be my first choice of a dive op (not because anything is wrong with them), but it sure is convenient. I agree with what has been said by
@KathyV and others about the diving. On the other hand, saving $25 a day on a 2 tank dive is an important consideration, especially since you have a car. Having been in GC during the time of year you're going and even driving into Georgetown when cruise ships were in, I'm one who never thinks the traffic is bad...it's all about being patient.
Although you're not doing the all-inclusive, you can still purchase meals at CC. It's as expensive as a good restaurant elsewhere on the island, but is pretty good. If you've read reviews about CC, you know there is not anything to do there, other than dive. Hell is about a 15 minute walk, or 5 minute drive. The Cayman Turtle Center is about a 10 minute drive from CC, as well as Macabuca which has been mentioned by others already. There is a dive op there (can't remember the name) where you can shore dive or even get a night dive in. The Turtle Center has a section - cost a bit more - where you can snorkel, swim, and/or layout in the sun. It has been one of my favorite places to snorkel with a guarantee of swimming with turtles and reef fish. If your sister snorkels, she might like this. Other things to do: jetski tour with with a stop at Stingray City, and Rum Point, Starfish Beach, Botanical Garden, and Cave tour on the East End.
I have attached a link to a thread I started that may give you some extra info as you read through it.
Grand Cayman: Cobalt Coast (Reef Divers) and Compass Point (Ocean Frontiers)
Any idea of things maybe going on for New Years Eve?
We arrived on New Year's Eve a couple of years ago and went to Camana Bay for their big bash. Music, restaurants, and fireworks. I actually booked a restaurant several weeks in advance of our arrival. We had a good time hanging out there.