Reddit reviews AMC's Best Day Hikes in Connecticut, 2nd: Four-Season Guide to 50 of the Best Trails from the Highlands to the Coast

I like Valley Falls in Vernon. Mansfield Hollow is solid. Backpacking up at Bear Mountain in Salisbury.

In the south, I really love Westwood Reserve in Guilford.

I'd highly recommend you pick up AMC's Best Day Hikes in Connecticut, they have some great recommendations all over the state, including specific loops and what's on them.

This book is pretty good https://www.amazon.com/gp/product/1934028770/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1

Second the Appalachian Trail tip with an additional shoutout for the ATC paperback book that serves as a MA/CT guide. It points out loads of detail on trail areas as well as identifying trail shelters and primitive campsites.

The tough thing about finding good dispersed camping in CT is basically that it's all there out in the open but there aren't a ton of good resources for organizing that information. I've been trying to figure this out myself a lot more recently because I just moved back from living in PA a long while. Most of what comes up when you look online is what appeals to RV campers and families: KOA campgrounds and the like. That's where business is so that floats to the top of a web search.

I'd suggest starting with this one, and then also you might find some info here, but even though the second book is mostly focused on day hikes it still identifies places to camp, if i remember correctly.

As for specific places, I can recommend Sage's Ravine, which sits on the MA/CT border. There's a nice set of sites there and it's all easy to use. There are bear boxes for protecting your food without having to rig a bag. I'm also fairly sure there's a no campfire policy. I wouldn't suggest messing with that if you plan to go, though I'm also fairly certain I've seen some people with small fires there now and then.