Okay, the UCC University… Of course! 
The Lakeland College I know is south of Urbana Champaign.
An advantage of Lakeland University is that it offers co-ops and co-ops aren’t deducted from OPT.
Full tuition scholarships at colleges that don’t meet need are always predicated on merit (even if they have a need component) but since, as per College data, Lakeland University is open admission and the 25-75 ACT is 16-22, you should have no trouble winning a merit scholarship there. The issue will be whether it’s open to students on a visa and whether your graduating from a local HS can qualify you for something.
Have you talked with your host family and would they be willing to host you again? That’s something you need to be sure of.
What colleges are commutable from where they live?
Beside the colleges I listed, you could apply to Berea (it’s a topnotch college dedicated to smart students from families that make under 65-75k a year). They admit one student per country at most but I doubt they have many applicants from Mongolia.