Yes, Tulsa would be a great full-ride safety.
Also check out the National Merit package at UT-Dallas. It isn’t small and rural (suburban, with 21K undergraduates), but it’s “nerdy,” and you’d be in the Honors College which, with 1300 students, is the size of a small LAC. Large percentage of Asian students here (if I’m guessing correctly from your username, and if that matters to you.) If you’re torn between life sciences and tech, you might check out their Cognitive Science major which has both computer science content (the school’s greatest strength) and bio/neuroscience content, with students choosing their concentration within the major.
Another smaller, “nerdy” school where you’d get big merit is U of Alabama Huntsville. It isn’t rural, but it’s in the Appalachian foothills of northern AL, so there’s lots of nice nature nearby. Only 7K undergrads, and great for STEM. It wouldn’t be a full ride, but it could well be in-budget - run the NPC and see.
Tulsa and UTD are D3, and UAH is D2, so depending on your sport, they might have athletic possibilities for you also.
Clarkson is a small, rural D3 school that’s strong for both engineering and pre-health. They don’t guarantee full-need-met aid, but they’re fairly generous with merit, so it doesn’t seem farfetched that you could get the aid you need here through a combination of need-based aid and merit. It would be a safety admissions-wise; run the NPC to see how it looks money-wise.
Harvey Mudd fits the pattern of schools that interest you (small and nerdy but part of a larger consortium with 7K students total. Not rural, but quiet suburban. Similar rigor to nearby Caltech but far more undergraduate-focused.). Its D3 teams are shared with Scripps and Claremont McKenna. Run the NPC to see if the aid would be sufficient.
Union in NY could be worth a look. D3, meets need, has engineering, but has only 2100 students. A little more urban than you want, but it has lots of green space, and Schenectady isn’t an overwhelming city.
Have you considered Swarthmore and/or Lafayette? Seconding Rochester too.
JHU and Penn are pretty urban for what you say you want; have you considered Dartmouth? (Not “nerdy” per se but at least rural.) GT is nerdy, for sure, but very urban and likely not affordable unless you get one of the ultra-competitive Stamps scholarships. Purdue doesn’t seem “safe” financially. Also not sure how UIUC or UMich would be affordable. UVA and UNC are the only OOS publics that meet need. Has your counselor helped you to assess affordability?
You have safe in-state options in NJ though, which hopefully would be affordable, plus the big merit schools.
You didn’t specify gender, unless I missed it; Smith has engineering and could be a great option if you’re female.
Good luck - let us know what you’re thinking after looking at the suggestions that have been made.