Lots of great places, though you would have to check which ones are open for lunch tomorrow. Pizza is the the local specialty, but there are great restaurants in every style. Did you ask grandma if she has a favorite place, or one she has been wanting to try?

Right down State St from Hamden into New Haven you have a bunch but I think you’ll be happy with September in Bangkok ( delicious if u like Thai food), plenty of street parking; and NOLO aka DaLegna at NOLO ( good pizza but plenty of other stuff too and a good dessert Ice Cream sandwich treat for Grandma). NOLO has on site parking. Both are spacious, easy to move around inside for all ages. Good luck

Prime 16 burgers, geranimos, jacks steakhouse, Bar, pasta cosi

I don't know of any that provide an old lady and a toddler, you might have to bring your own.

Go for pizza

Do you like Italian? Go to Adriana’s in New Haven

Eli’s, townhouse diner

This screams diner to me.... I love the Parthenon in Branford, or Twin Pines.in East Haven. As a mom it has everything, is casual, AND EASY PARKING! Less diner and more restaurant is Eli's on Whitney in Hampden.

It’s worth noting that Mamouns - Falafel, kebabs, hummus - is open 365 days of the year. It’s a good spot if you like Middle Eastern, they do it well and it’s a good casual sit down place for lunch.

Sherkaan is open for New Year’s Day brunch

Mikro in hamden is doing a New Year’s Day brunch from 11:30 to 3. You’ll need a reservation though.

In Hamden: Cafe Amici, Elis, Mikro, Playwright (if Irish and American pub food works for grandma and child)

https://www.tripadvisor.com/Restaurant_Review-g33801-d2358530-Reviews-Cafe_Amici-Hamden_Connecticut.html

Nolo, Prime 16, Camacho Garage, Rudy’s, Crepe Choupette, Bella’s, Heirloom, Archie Moore’s.

MiKro in Hamden is doing brunch until 3pm!