This is pretty good list, the only things I'll add: Pepes and Sally's are better than Modern, and on one street with a great Italian dessert spot from 1915 (libbeys). These are walkable from downtown, as Modern is farther. Other bars with good vibes are Old Heidelberg, Rudy's. He mentioned Three Sheets which is a classic. I'll also add that Cafe 9 is great but demands a cover usually so if you're popping around and don't want to drop 10 bucks per person keep that in mind. The axe place closed. Barcade is not unique to new haven but pretty cool. I would add Ordinary as a cocktail bar, but get a reservation.

Bar is another famous pizza spot, has pool and brews their own beers, and transmogrifies into a dance spot in the back at night.

Have fun