Without writing a book, I'll try to add some insight here. I lived in central and eastern Connecticut for 25 years, moved there to go to UConn and stayed. Mrs. BDT grew up there. Finally left 10 years ago to move 400 or so miles south. I go back there at least twice a year on business and to visit friends - I don't really think things have changed much.
First of all, there are some really nice aspects to the area. Once you get outside of the urban centers, most of the area is very pretty - sometimes postcard pretty. There is some suburban sprawl but there are lots of areas that are semi-rural. Location is everything and there are dramatic differences between one small town to the next. Affordability will definitely be a challenge to land yourself in one of the more desireable towns - Avon, Farmington, Glastonbury are all out of sight. Windsor and Windsor Locks are bedroom communities - more suburban and somewhat more affordable. Suffield and East Windsor are less densely populated.
There are still lots of ethnic cohesion in certain areas. The south end of Hartford has a big Italian community, lots of Polish people in New Britian, and I could go on - but I'll be careful here. Multi-generational families still live within walking distance of one another in many parts of the state. The best part of this is the food opportunities. Italian bakeries, Jewish delis, etc. The thing we miss most about Connecticut is the food: pastries, pizza, bagels, Jamacian, and so on.
Keep in mind that there are 168 or so separate towns in the state and each has its own separate government. There is no county government at all and everything - schools, police, garbage collection, library, etc. is done at the town level. This means significant variation in levels of service from one town to the next - so be choosy about where you settle. It also means high property taxes because there are no efficiencies of scale.
Culturally, the Hartford area isn't bad. There are good museums, concerts, shows and LOTS of history in the area. Plus, both New York and Boston are relatively easy day trips.
Recreation is also good. The mountains are close by for hiking and camping, as is the LI Sound for boating, swimming, fishing and seafood. Excellent fly fishing nearby. If you like to ski, you can be in southern Vermont in less than 90 minutes. If you like casinos, there are two really fancy ones an hour away.
Autosports - I'll let others with more current information weigh-in but of course Lime Rock is close by and I believe they do a 24 of Lemons at Stafford.
So what's the downside? Well, you've already identified a couple of issues. Cost of living is very high - not just housing but everything! The first few winters will be fun because of the novelty, but then they start to wear you down. Put the heat on in September and don't plan on opening the windows again until May. Light, powdery snow is nice. Wet, heavy snow - not so much. Wet heavy snow, change to rain, change back to snow and then drop 20 degrees and freeze solid as an ice cube... you can have it!
Package stores close at 8 pm and are closed on Sunday. You can't by beer, wine or liquor except in a bar after 8.
Also, we found that the people are hard to warm up to as well. I lived across the street from a guy for 5 years and never once did we have a conversation beyond "how ya' doing - crappy weather, huh?"
The cities themselves are not very nice and can be dangerous if you stray into the wrong parts. If you are familiar with Philly, Hartford, New Haven and Bridgeport will be deja vu all over again.
I know plenty of folks who have lived there their entire lives and would not THINK of going anywhere else. I also know plenty of folks there who have never BEEN anyplace else.
During your visit - get a good thin crust pizza from an Italian joint (not a thick crust Greek pizza, still good but not the same). Get a cannoli - preferably from someplace where they don't speak very good English. Get a lobster roll if you can. Go back to the Greek place, tell them you still don't want a pizza but ask them to make you an eggplant grinder.
Take Rte 75 north from the airport up to the Mass border. It is only about a 20 minute drive - it is a good basic idea of what the area can offer.
Have fun and good luck with your interview.