Try just outside Hartford to the North. Windsor, Ct.
I was in Hartford a couple of weeks ago, for the first time in 15 years, and I was shocked at the overall degeneration of the downtown area. Not a place I'd like to be at night, even with my (legally carried) pistol. As for East Hartford or New Britain, FORGET IT!!! The suggestion about going North (even as far as Windsor Locks) is a good one, I think. Still pretty rural and small-town New England, unlike the bigger cities (especially stay out of New Haven and Bridgeport). Democratic rule has destroyed most of the cities in Connecticut and Massachusetts- and you are not immune from being mugged or killed if you are a Democrat ("Oh, wait, don't hit me with that bat- I LOVE you inner-city people!")
If you MUST live close to the Law School, then probably the West Hartford / Farmington Avenue suggestions are good ones. But the only good thing about Hartford is that you can get to New York easily from there...
Negative on the Windsor idea. Most of Windsor and Bloomfield have gone the way of the north end of Hartford. West Hartford is probably the best option.