I think that J Tims keeps the best taplist and is also fairly price appropriate, though not that close to Hartford proper.
Based on my experience (I work in Hartford and live in Newington) and would say that J Timothy and McLaddens are the best overall taplists in the area, with my preference far leaning to J Tims for the experience and price. Also J Tims wings and tailgate pretzel are almost too good.
Tavern and Rooster Co usually each have a decent option or two on but not more than that. Trumbull is a cool spot for food but the taplist is short and generally not too interesting. If you want to catch a beer at Rooster (or anywhere that has been mentioned, really) please let me know!
A sleeper spot is Prospect Cafe, which usually has a pretty tight taplist (and tons of good eats nearby). Glastonbury's Birch Hill Tavern is also a very solid bar, though not in the immediate area (still as close as most of those mentioned). If you are going as far as Manchester, I would add Lucky Taco to the list of potentials.
Edit: Eli Cannons is about 20 mins from Hartford and generally has a pretty stacked list. I have found New Park Brewing to be a decent spot to eat food truck food, grab a pint and fill growlers (Hazy IPAs and berliners) any time Thursday - Sunday.