I only know of a couple local brew places around Hartford. Theres City Steam Brewery right in the city. They have about 10 or so beers available. Only been there twice so can't comment too much on there beers. I think there brown ale (naughty nurse) is there best selling one. You also have the Hooker brewery in Bloomfield which is just north of the city. Never been to it but I'm sure they would have tours and tastings. All else fails Hartford is just under a 2 hour drive to Boston.
In Hartford proper -
The Half Door / Irish pub with mostly European beers on tap (including belgians) and great bottle selection
In Hartford Burbs -
Eli Cannons / Middletown 20ish minutes outside Hartford (good food and a GREAT variety of beers represented)
Plan B / West Hartford (great burgers and great rotating beer selection)
The Cambridge Brew House / Granby 30ish minutes outside Hartford
Willimantic Brewing Company / Willimantic, CT 45ish minutes outside Hartford
There are others that are escaping me at the moment...