How long it takes really depends on what you intend to do and how long you take to do that. I guess there are some practical hard minimums based on driving speeds and times, but even so what's a reasonable minimum length for such a trip varies a lot based on who's driving (and if you have more than one driver to share the duties).
Personally, I'd likely plan a minimum of five days each way between CT and one of those states, which leaves basically no time for doing anything along the way besides eating and sleeping. (Four days might barely be possible for me, depending on the final destination.) Anything much less than about three weeks would seem to me to not be worthwhile for the trip, assuming the goal is tourism/vacation; with less time, I'd opt to fly or take Amtrak out or something, or choose a destination closer to home.
You, of course, may cover more or less distance in a day comfortably than I do.