Are there any "good" schools that like to see transfer students who made a major improvement?

After I started college, my depression got really bad and I crashed and burned. Hard. Between the stress of that and working almost full time, I was failing and withdrawing from classes left and right, skipping semesters, etc. My completion rate was something like 48% after 3 years (in a 2-year program lol which I enrolled in because my school misled me, but that’s a whole other story). But then I got help, turned my life around, and made a complete 180. Got an A and B in the first couple classes I took to ease myself in, and now I’m on track to make straight As and believe that I can maintain that for the rest of my time here. My GPA will have gone from the low 2s (or maybe even high 1s, I can’t remember exactly) to around a 3.4. My performance in high school was pretty mediocre too (3.45 UW), though I did have one impressive EC. Is it too late for me? I’m not that worried about it because I’ve got guaranteed admission to my local university through a program they have with my college, but I’d like to aim a little higher than just…the university that happens to be there.

I’ll of course also be applying for the good schools in my state as well.

What do you want to study? Where is your local university?