I don’t think most people equate “Northeast” with New England. To me, New England is a subset of Northeast. (And New England has a very straightforward definition: CT, RI, MA, NH, VT, ME.)
But where the southern border of “Northeast” lies is open to debate. (Obviously, lol.)
All that matters is what counts as “northeast enough” to the OP. And whether they’d consider “northeast adjacent” options if the price is right. (Also worth noting that they said “especially” northeast, which doesn’t necessarily mean exclusively northeast.)
But there’s really no point squabbling about what the boundaries should be if OP isn’t going to clarify their criteria.