Broad street diner is on... Broad street, not too far from the arena and family friendly. Used to eat there a lot. There's also Angie's in bordentown but that's a bit south of the arena. I think pats diner has alcohol but the diner is low quality and icky. Killarney's in Hamilton is a bar that I often went to with my kids, and is my biggest suggestion. Their food is great.

Basically don't look in Trenton, try Ewing and Hamilton instead.