Second Street Bakery 402 2nd St, Italian, wonderful sandwiches on their own bread, they close early
Philippine Bread House Cafe 530 Newark Ave, baked goods and plate lunches
Pecoraro Bakery 279 Newark Ave, good bread and focaccia
Carmen Rosa Bakery 37 Coles St, sugary dominican treats, incredible value. My daughter vouches for the red velvet cake
Cinco De Mayo 401 Central Ave
Los Tres Chilitos Mexican - 456 Central Ave
These 2 Mexican restaurants in the Heights are sometimes uneven, as staff come and go and communication can be an issue if you don't speak spanish, but if you're willing to take a chance, and if you find out what the specials are, the food can be delicious.
There's White Star for a burger and a beer http://whitestarbar.com/
Indian in Jersey City, well there are quite a few places in close proximity and I can't say I've ever had a sublime meal, but not a bad one either, and I've just tried a place that would be fun for the adventurous, China Chowk. It's an Indian take on Chinese food. The sauces were a bit gloppy, but I'd like to explore the menu further, especially more of the appetizers and the "drier" dishes.
I agree on most of the other recommendations except for Hard Grove, which is terrible.
279 Newark Ave, Jersey City, NJ 07302
Hard Grove Cafe
319 Grove St, Jersey City, NJ 07302
Philippine Bread House
530 Newark Ave, Jersey City, NJ 07306