There are three shops right in town, College St Cyclery on....College St, right downtown; the new Devil's Gear in a large space on Orange at the bottom of the new giant 360 State building; and then Amity bike's New Haven post out on Chapel St in the Wooster neighborhood (where Devil's Gear was before their move).
Get a little further out, and you've got North Haven Bikes, the original Amity Bikes up Whalley, past Westville, and a place who's name I am forgetting that is out on Boston Post Road.
Even further out and there are a couple more notable shops.
New Haven's Critical Mass rides are pretty fun. There are mtb trails close to town at East Rock and West Rock, and plenty more in short striking distance. Most trails are unfortunately still pretty snowy and icy, though, and after the thaw it'll be a trail-killing mudfest for a while.