Just a synopsis of what's going in CT post Sandy Hook, since I get asked a lot.
1) Handguns (revolvers and pistols with a magwell in the grip) can be brought into the state for formal pistol and revolver training, provided you have a carry permit from your home state. They have to be transported unloaded and in a locked case in the trunk. Travel must be direct between hotel/home and training facility.
2) Handguns can't have threaded barrels, unless the handguns were lawfully registered as "assault weapons" pursuant to SB 1160.
3) All magazines (rifle and pistol) have to be 10 rounds or less, unless they have been registered pursuant to SB 1160. Off-duty LEO's covered under LEOSA 2004 have to comply with this (but probably wont catch any grief from other LE's). Exemption: FFL's, active duty military and on duty LE.
4) It is unlawful for a private citizen to import an "assault weapon" AND/OR ASSAULT WEAPON PARTS into the state unless it was registered pursuant to SB 1160. This is basically all black rifles (even in postban configuration). Exemptions apply to FFL's, active duty military, and to a certain extent LEO's.
5) When in state, non-residents can no longer purchase ammunition or even ten round magazines without one of the following CT issued permits: 1) pistol permit, 2) rifle permit, 3) ammunition eligibility certificate. These permits are issued by CT DPS to non-residents (just apply for the pistol permit, our "CCW.").
So to recap, for non-residents:
1) Handguns (revolvers and pistols with a magwell in the grip) are fine if you have a home state CCW, no threaded barrels. Unloaded, locked in box, in trunk, direct trip from hotel to range and back (no stopping).
2) 10 roung mags only (this applies to both rifle and pistol)
3) Do not bring black rifles AND/OR ANY PARTS into the state
4) Bring your 10 round mags and ammo with you as you won't be able to buy them.
If you travel into CT a lot, do yourself a favor, apply for a CT pistol permit. In practice, CT is shall-issue. All that's required is a clean background , proof of training, and a state CCW (doesn't have to be your home state). A lot of folks from NJ, for example, get CT pistol permits using UT non-resident. Max turnaround time is 8 weeks. Some folks in NY have gotten theirs in 3.
http://www.ct.gov/despp/cwp/view.asp?A=4213&Q=530224
Non-Resident Application for Pistol Permit; Call for a complete packet which includes fingerprint card at
860-685-8290.
CT off-limits places include schools (as defined, K-12) unless you have the permission of the principal, wherever signs are conspicuously posted, courthouses, and while bow hunting.
While bars are not off-limits by statute, it is a crime to be in possession of any loaded firearm if "the ratio of alcohol in the blood of such person is ten-hundredths of one per cent or more of alcohol, by weight."
Open carry is legal in CT, provided you have a valid CT pistol permit.
ETA:
Regarding Bradley International Airport (BDL):
I have had no issues flying out of BDL with firearms (evil black rifles, pistols, mags) so long as TSA was inspecting the guns at check-in.
If a CT state trooper is standing watch, HE WILL INSPECT YOUR STUFF FOR COMPLIANCE.
Take note.