You DO need to know the exact range that your parents mean. NOT a vague assurance they can afford it. 50-70K a year ok? Or 50-55K? Would 45K be better? (UIUC is about 40K instate, I think)
Another issue is that having a good life as an elementary school teacher and living in the South are two things that are almost antinomic… :(. You’ll need to research carefully.
Since you wanted top-level schools, all of these (below) would be hard to get into, but the ones with * are “reach for everyone regardless of stats” so they should be the last added after you have found to affordable safeties you like, and 3-5 matches.
Vanderbilt is the obvious one but it’s “dream school” category.
*Davidson has an Education Studies minor that you add to your major of choice. Professors advise you to be recruited by TeachForAmerica or TeachCharlotte or independent/private schools. (They’d clearly heard about the horrible conditions in public schools in NC).) Davidson is smaller than what you want but it’s the most prestigious southern LAC, it’s very jockey, it’s near a thriving city, it’s southern, and it’s as elite as you can imagine. 
https://www.davidson.edu/
Elon has a 4-year certification. Its atmosphere and vibe sounds exactly as what you’re looking for.
https://www.elon.edu/u/academics/education/
Rhodes has three tracks for education
https://www.rhodes.edu/education
*Rice has a “make your own minor” education studies program, or you can get your Bachelor’s+ MAT in 5 years.
https://ga.rice.edu/programs-study/departments-programs/continuing-studies/teacher-education
*UT offers everything but it’d be a definite reach since there are so few spots for OOS applicants.
https://www.utexas.edu/academics/college-of-education
Trinity TX has a minor you can add to your major, which leads to a 1-year MAT.
https://new.trinity.edu/academics/departments/education/master-arts-teaching/minor-teaching
*In cold climes, but worth checking out: Brown
https://www.brown.edu/academics/education/
UF (Florida) has everything
https://education.ufl.edu/
8 Tracks at Florida State, including accelerated BS/MAT program
https://education.fsu.edu/degrees-and-programs/undergraduate-programs
Rollins offers Elementary Ed certification&licensure (BS only)
http://www.rollins.edu/academics/areas-of-study/undergraduate/education.html
UMiami has a special program where you get both Elementary and Exceptional education, which can include TESOL
http://sites.education.miami.edu/elementary-education/
At UGA, some education majors are “selective access”, meaning that unless you’re interested Math&Science education, you may not get into the education major you want… The *Honors college DOES allow you to “build your own major” but you will need 1430+ on the SAT plus excellent course rigor in order to get into Honors.
https://coe.uga.edu/directory/departments/math-science-education
https://coe.uga.edu/
Agnes Scott does let you have an Education minor and support to get into a GA “fast track” program
https://www.agnesscott.edu/education/majors-minors.html
https://www.gapsc.com/EducatorPreparation/GaTAPP/GaTAPP.aspx
USC Columbia has one of the top *Honors colleges in the country but South Carolina is pretty bad in the way it treats its teachers. One program for K-4, one program for 5-8.
http://www.sc.edu/study/majors_and_degrees/middle_level_education.php
http://www.sc.edu/study/colleges_schools/honors_college/
*UVA offers a very interesting program on top of a Certification or major, Global Studies in Education.
https://curry.virginia.edu/academics/undergraduate
*William&Mary has TESOL
https://www.wm.edu/as/modernlanguages/minorinteachingenglish/index.php
Virginia Tech has “education pre-major”
https://vt.edu/academics/majors/pre-education-and-human-sciences-undecided.html
In California,
UCSC has a minor (or a “science education” concentration) - California requires you get a MAT.
https://education.ucsc.edu/
SDSU has two options, one where you can teach 4-6 or one where you can teach 4-8.
http://arweb.sdsu.edu/es/admissions/majors/liberalstudies.htm
UC Davis (North) only has Physical Education
https://ls.ucdavis.edu/interdisciplinary-programs
Sonoma State has the Hutchins Program, a sort of interdisciplinary Honors Program that is especially well-suited for teachers. Would be a safety for you.
http://web.sonoma.edu/hutchins/
UC Santa Barbara has a minor for Teaching English to Speakers of Another Language
https://my.sa.ucsb.edu/catalog/Current/Documents/2017_Majors/LS/Ling/Minor_TESOL_2017.pdf
Cal Poly SLO has an Elementary School preparation program (+1-year MAT)
http://catalog.calpoly.edu/collegesandprograms/collegeofsciencemathematics/liberalstudiesanundergraduateteacherpreparationprogram/
UIUC Elementary Ed is likely a safety but you need to find another one.
Add a few good flagships - perhaps pick 1-2 from these: UVermont, UWisconsin, Indiana U, Penn State, Ohio State, Michigan State… and pick others from the non starred universities above.
Always apply to the honors college.