Well, Cincinnati is your portfolio-free Drexel alternative. Also urban, also a co-op program. It’s definitely worth looking closely at both Cincinnati and tOSU - compare the programs and see what you think. And if being a bit outside the city is okay, Miami of Ohio could be worth having in the mix as well: Bachelor of Arts in Architecture | Dept. of Architecture and Interior Design | Miami University
Conn College is great, and they do give merit, but I don’t see them making a 30-40K budget. At any of these merit-granting private LAC’s (Smith, Bryn Mawr, Conn…) it’s very competitive even to get to half-tuition merit, and that doesn’t even get the total COA down to 50K much less 30-40. (And Amherst College doesn’t give merit at all, so I don’t see the point in having it on your list. You could consider UMass Amherst, though: https://www.umass.edu/architecture/academics/undergraduate-programs.)
If you’re liking the women’s college idea, but not seeing it come together because 1) too expensive and 2) parents not loving the single-gender idea, you might think about Rutgers. When the all-female Douglass College was merged into the flagship U, it was transformed into a women’s Residential College within Rutgers, which offers a single-gender living community and tons of great programming: https://douglass.rutgers.edu/ Rutgers doesn’t have an arch major, but their Urban Design & Planning major does have the design piece and seems pretty close to what you’re looking for. There’s also an Environmental Planning major that’s offered by the LArch department. You’d need about 15K in merit to get into your budget range here - I’m not familiar enough with the merit landscape there to assess whether that’s likely, but perhaps others will chime in.
Also, maybe consider UVM? Burlington isn’t urban by NYC standards, but it is a city, and a pretty great college town. Community Centered Design Major | Community Development and Applied Economics | The University of Vermont OOS merit awards that would get you to budget do exist, although landing 5-10K over budget is more likely.
There are quite a few on your list that are, tbh, not worth your time applying. Northeastern, for example, is absolutely not going to be in budget. Even their NMF package wouldn’t make it affordable, and all other merit awards are even smaller. You wouldn’t even be likely to be admitted directly to the Boston campus - if you got in at all, you’d be full-paying (more than double your budget) to spend your first year abroad or in Oakland, thus blowing your geographic boundaries as well as the financial ones. Sorry, but Northeastern is a nope. (Again, Cincy is the more-affordable co-op substitute.) Neither BU nor NYU will be affordable either. And why debate about the geography of Notre Dame and WashU? They won’t make budget either. (WashU gives a few highly-competitive merit awards but you wouldn’t really be in the running for those - getting in at all is reachy.) CWRU does at least give a fair amount of merit, but getting in and getting enough merit makes an affordable offer there a high reach. (It’s worth applying if you love the school, but make sure you show them that love - they really care about demonstrated interest, and track whether you open their emails, click on links, etc.)
And some of your OOS publics are pretty pricey too. UMD, UVA, UIUC (which is also too far and not urban)… none of these is going to get under 40K for you. (Hopefully others will correct me if I could be wrong, but I don’t see how you get to budget.)
I’d suggest trying to get out to Buffalo for a visit, if you can. This seems like your guaranteed-affordable, best-fit in-state option that sets the bar for others to beat.