Unstable college history turned around - where to transfer?

Please, help. I am so confused.

Out of HS I went to Columbia Chicago and withdrew my third semester because of medical problems, then went home to Texas Women’s and withdrew (or failed out, I can’t remember) the first semester there because I needed a follow-up surgery. That all happened in Fall 2013-Spring 2015.

In Spring of 2017, I went to a VA community college and ended up getting an associates of applied sciences in paralegal studies. I applied to William and Mary for spring transfer and didn’t get in (presumably because they don’t take many spring transfers and my degree wasn’t transferable). I went back to VCCS to take a few extra classes and get a second associate of science in general studies- a degree that DOES transfer.

Now I’m reapplying to W&M, but I also want to apply to other schools as well, just in case. I’m interested in majoring in public policy or history, then maybe minoring in philosophy or political science.

I’m a Virginia resident, my VCCS GPA is a 3.92.
When I did take the ACT back in 2012, I got a 33 composite (if that even matters it was so long ago)
I’m hoping to go on to law school eventually, hopefully to a t14.
In all, I’ll be transferring in with two associates and graduating summa cum laude with both.

What other schools are in my ballpark? Will my shoddy academic history keep me from getting in to a good school?

I was looking at UVA, St. Mary’s Maryland, George Mason, James Madison, Wake Forest, Loyola Maryland, then possibly a couple in New Orleans (Tulane and Loyola NOLA).

I want a challenging, reputable school with a good social scene.

Ideally near water (I love to sail), near a national park like JMU, or near DC because I want to be in the legal field. It has to be somewhere that will look good on a law school app!

I missed the deadlines already for Uni of Richmond and UNC Chapel Hill.