Yeah, they can be very generous with the need aid, but that is not helping the OP.
That list Thorsmom66 linked is pretty interesting, though. At least at some SLACs, the kid would likely qualify for the highest merit, so even more than average. And the ones with both reasonable percentages receiving merit and high averages in relation to full COA are not the most famous Northeastern ones, but still some really good colleges–Beloit, DePauw, Wooster, Juniata, Ursinus, Centre, Allegheny, Wabash, Kalamazoo, Ohio Wesleyan, Lawrence, Cornell College, Agnes Scott, Hendrix, Rhodes, Knox, Washington College, Whittier . . . . those are just the ones I spotted on one page (ranked by average merit).
Again, not necessarily BETTER than in-state, but lots of potentially affordable options for different.