You may or may not have heard of it, but Pepe's is widely considered to be the best (or at least in the top 5) pizza places in the US (hate to break it to you, Chicago and NY friends...). Even a jamoke will tell you that you should try the white clam pizza. But show up early, the line gets long very quickly (it's always worth the line).
After you've consumed a few slices of white clam pizza at Pepe's, take a walk over to Libby's for a pastry or two (try a cannoli, ya scungill). Bring cash!
Once you've exhausted the two Starbucks locations 1,200 feet from each other (no kidding, google it), try a good local coffee shop that doubles as a bar late at night.
If you're okay with having pizza twice in one weekend (most of New Haven is, no worries), go to BAR Pizza. The same jamoke who recommended the white clam from Pepe's would recommend the mashed potato pizza with bacon. They also brew their own beer. BAR also gets packed pretty easily, try to get there early.
This is a great brewery right on the water in Branford, about 15 minutes from downtown. It'll be the perfect time of year to sit out on the deck with a beer and see the leaves change.
Whereas BAR is an upscale, downtown brewery, go to THC for a spacious beer garden with a firepit, cornhole, great beer, and clam pizza (not as good as Pepe's, but don't go here for the pizza). You can probably find us there on Thursday night before the wedding, it's a great hangout.
They don't serve the best hamburger, but they served the first hamburger (https://www.eater.com/2015/4/15/8414107/louis-lunch-new-haven-connecticut-burger-invented-history). No ketchup allowed. It's about the size of a walk-in closet, so leave your elbows at home.