I've never been to New Haven and I'm a little overwhelmed by all the hotel options. I'd like to stay in a hotel that is central and gives me good sense of what New Haven is like. I'd love to know where locals tell their friends to stay when they visit, and why those areas and hotels are special. thanks!
You have to get pizza! Its the best. There is pepes or sallys on wooster st. Or Modern pizza.
Mentioned in this answer:
The Study at Yale Hotel would be my first choice; however is not going to be your lowest cost. They have a great restaurant Heirloom on the first floor for a drink and small bites. Still centrally located, but at a lower cost would be New Haven Hotel. Both allow you to easily walk around town and are close to many food options.