So, my brother and I thought about going to New York City in January, but it's looking less possible now since he hasn't gotten a post-graduate job yet. My brother isn't cash strapped, but he's reluctant to spend a lot of money without a steady source of income. Is there a time of the year besides January where things in Manhattan are relatively affordable and won't end up costing more than 2 grand?

Yes. February.

Hard to answer questions with no details what so ever..