I'm not local, but here are some resources you may look into:
A list of gem/mineral clubs in Connecticut. I'm sure that other /r/rockhounds will back me up when I say that joining a club is a great way to meet people who know where to go to find the goods. Clubs also often go out on field trips periodically.
A list of upcoming mineral shows. According to that list, there's one coming up in Greenwich, CT on 5-6 November! Another solid place to meet some folks who might give you some pointers, and a great place to get your Christmas shopping done!
GatorGirl's list for general-interest geology stuff in your state. You might cut your teeth on one of the two commercial sites listed at the bottom there before venturing out on your own.
Peter Cristofono's <em>Rockhounding New England</em> guidebook. I'm not familiar with the author, but it seems pretty well-reviewed on Amazon. It claims to offer GPS coordinates for sites, which is an absolute godsend if you've ever tried to follow bad directions on an unmarked county road to a tiny outcropping in the middle of nowhere. You may be able to find a copy at your local library.
And here is the full Mindat page for finds listed in your state -- towards the bottom, you can sort by county. Mindat's pretty comprehensive and often has great pictures to help you know what to look for when you hunt, although many of the specimens were collected from private land or closed sites.
Happy hounding!
Rockhounding New England: A Guide To 100 Of The Region's Best Rockhounding Sites (Rockhounding Series) https://www.amazon.com/dp/0762783656/ref=cm_sw_r_other_awd_6X26wb5VVT2AP
Rockhounding New York: A Guide To The State's Best Rockhounding Sites (Rockhounding Series) https://www.amazon.com/dp/0762779004/ref=cm_sw_r_other_awd_KY26wbYF584VV
Roadside Geology of New York (Roadside Geology Series) https://www.amazon.com/dp/0878421807/ref=cm_sw_r_other_awd_dZ26wbRZZCT7B
The Collector's Guide to the Minerals of New York State (Schiffer Earth Science Monograph) https://www.amazon.com/dp/0764343343/ref=cm_sw_r_other_awd_DZ26wbH96TSC2
I've found rockhounding books usually have good intros and brief explanations which is good for beginners.