Day one
For lunch or an early dinner, go classic and head to Wooster Square. Frank Pepe Pizzeria Napoletana, 157 Wooster St, and Sally's Apizza, 237 Wooster St, are both verified staples there. If you want another pizza option nearby, Zeneli Pizzeria is at 138 Wooster St.
At night, downtown gives you a few easy choices without overplanning it. Bar, 254 Crown St, works if you want a bar that also serves pizza. Ordinary New Haven, 990 Chapel St, is a craft cocktail bar. Anchor Spa, 272 College St, is another cocktail stop with a long history in the city.
Day two
Make the second day a neighborhood day. In East Rock, Olmo, 93 Whitney Ave, is a bagel shop known for handcrafted bagels and breakfast sandwiches. If you're around State Street later, Modern Apizza, 874 State St, and Tavern on State, 969 State St, are both solid anchors for a meal.
If you'd rather stay downtown, there are enough verified dinner options to keep the plan flexible: Union League Cafe at 1032 Chapel St, Heirloom at 1157 Chapel St, Olea at 39 High St, and Strega at 1006 Chapel St. That's a more useful way to build a weekend here anyway: pick one neighborhood, walk a bit, and don't try to cram the whole city into 48 hours.