Edit - there’s some new schools in here but just reading back the messages posted while I wrote - so there’s a lot of crossover with @AustenNut usual list of great sugestions.
This pretty much opens the gamut to most any “affordable” school. For example, you’d spend - let’s call it - at most $20K a year at U of Alabama which is over half OOS and draws heavily from the NE, midwest, and Texas. But it’s way too large and not close to where you want to be. A MS State is a much smaller but still larger but inexpensive.
A 10K student UAH will be $20K-ish a year based on automerit - but is certainly more regional then the other two. and strong in STEM. Or midsize UAB known for it’s medical activities.
Or a U of Tenn Chattanooga - also mid size and inexpensive for you.
So those type of schools would all crush your budget expectation.
Then there are the ones not as inexpensive - but still likely to blow away $50K.
SUNYs as an example (to hit your geography - there are many smaller ones (don’t know about sailing). Or a U Maine will come in at budget and it’s smaller.
A CNU in Virginia (very regional student body but very good school) or a Salisbury in Maryland will also easily make budget. Or a St. Mary’s of Maryland.
So those schools won’t be as cheap as the first list (well the in-state might) - but they sort of hit your size and geography.
Then there are the ones others mentioned - the private LACs - but the higher echelon - even the Connecticut College or F&M, etc. - could hit $50K but are unlikely whereas a Clark or Wheaton, etc. are more likely. In other words, hit the less competitive. I believe Gettysburg, as an example is aggressive.
But if you want LAC, then the midwest might be your best bet - the Allegheny, Wooster, Kalamazoo, Deapuws of the world - and more - are all higher cost but offer great merit.
I don’t think finding $50K, even in the NE, is a huge problem - but you are looking for “Inspiring” Matches - and I think that’s the hard point. More like you won’t even find inspiring safeties. - but just financial safeties - is what you can find.
But you can spend $20K if you want - or $50K.
But it’s easier to find assured under $50K schools than - top schools at $50K - because those top schools will always be “maybe” where others that I mentioned above are - with certainty. So a Connecticut College, F&M, Dickinson, or even a Rochester - could be $50K but are likely not to be - if that makes sense. So that’s the type you give it a try but go in with the expectation of not likely being able to afford attending (but a somewhat reasonable chance to afford, just not a high chance).
If you’re able to go a bit bigger, Miami of Ohio might be another to look at. Not sure if URI was mentioned as well - but would work financially, etc. It’s just a bit bigger.
Again, I didn’t put sailing into this.
Someone mentioned Charleston - it is more expensive - but your daughter might be a great fit for the Fellows Program (it’s a reach for Fellows) but comes with great merit although it’s not in your zone. Coastal Carolina would be a bit lesser powered school but also work. UNC Wilmington could be a fit too - a tad over 10K and not NE.
The point being - your student has afforded you dirt cheap or mid tier tuition - and yes, there may need to be some tradeoffs - but maybe not if a U Maine type is ok or various SUNYs or even regional schools like a MIllersville ¶ or TCNJ.
So the student has to decide what they really want - LAC, mid size - and is leaving a preferred geography ok to save my folks - a boat load - even vs. the $50K budget - if that’s something that interest you.
There are also - let’s call them hail mary schools - a washington & lee has the Johnson Scholarship - full ride. SMU the presidential - and there are others, etc.
The other thing is - even the “lesser” schools pedigree wise still have tons of opportunities for the kids who seek them out - my kid at Charleston is one example who has taken advantage of many opportunities available whereas other kids (like my son) - don’t. They just go to class.
Hope that helps a bit.