It makes sense that if you’re not attached to Florida, you might want to go ahead and make a move before you start college. You apparently have the resources to choose where you want to be, so there’s no reason to make that choice based on inertia, especially when you don’t qualify for the terrific scholarships that top students from FL high schools get in the FL public system.
However, I think your assessments of what target schools are “good” is rather naive and perhaps a little elitist. U of Florida is a top flagship university. There is nothing underwhelming whatsoever about its academic quality or reputation. I do not believe that an undergraduate psych major coming out of NYU would have any advantage in applying to grad programs over a UF grad with a comparable academic record, GRE, etc.
Now, if you said you wanted a smaller and more personalized college experience, and that was why the FL publics (and UC’s) did not appeal, I would be completely sympathetic with that point of view. It’s just… I’m not sure how NYU, with 26K undergraduates, epitomizes that goal. I think it’s true that a large private U like NYU will tend to offer smaller classes and less competition-for-resources in the first two years of college than a similarly-sized public U like UF or UCLA can provide, given that NYU is bringing in far more tuition money per student. But you’d be doing your first two years in community college anyway, and upper-division classes get smaller everywhere, private or public. Now, if you just want to be in New York City, that’s a different matter. But personally, if I wanted to get the most bang for my transfer buck in the state of NY, I’d aim for either Binghamton or Cornell, which accepts hundreds of community college transfers each year. Other great SUNYs to aim for would be Buffalo, Stony Brook, and Geneseo (LAC) There is great depth in the SUNY system; campuses you’ve probably never heard of would still give you perfectly fine preparation for grad school.
And then there are many excellent private U’s in New York as well (not that you have to transfer from a NY CC to get into these, but as you say, familiarity between the systems makes it slightly easier). URochester, Fordham, Syracuse, Vassar, Union, Skidmore (which has a particularly cool undergrad psych program IMO https://www.skidmore.edu/psychology/majors/paths.php )
Another nice thing about New York is that quite a few of the Upstate community colleges have on-campus housing, or private dormitories near campus.
The downside in aiming for small LAC’s is that many of them take very few transfers - sometimes zero in a given year. My daughter’s LAC just accepted some transfers this year, after returning application fees for the previous 2-3 years because they decided not to even read transfer applications. Plus, if/when you do get into a small LAC, you don’t have a large cohort of other transfers entering with you.
Anyway. My question would be, why was your HS GPA so low, and has something changed such that you can reasonably anticipate doing better in college? Projecting realistically is important, because you will need a solid GPA in your first two years to transfer to a competitive school.
If you need substantial work on your English and have money to spend, another possibility to consider is a Pathway program for international students, which would funnel you directly into a four-year university. These programs are advertised primarily for English remediation, but they take students whose stats aren’t competitive for regular admission as well. https://internationalpathways.northeastern.edu/about/ I am not aware that having your residency would be a barrier to enrolling in such a program, although I don’t know for sure. If you’re looking for a great urban university (as your interest in NYU would suggest), Northeastern would be an excellent choice. Entering Boston University through the College of General Studies might be an option too.
As you say, California has tons of options too; and you certainly don’t have to go to Berkeley or UCLA to get a strong undergrad psych education. You could go to Cabrillo College - the community college near UC Santa Cruz - and transfer seamlessly to UCSC, which is smaller and more personalized than UCB/UCLA. Or go from Irvine Valley College to UC Irvine. Santa Barbara City College to UCSB. Or, of course, mix-and-match… but if you want to have continuity within one community, you can do that. Also, many, many students from the CSU schools continue on to grad programs. You could get an excellent undergraduate psych foundation at many if not most of the CSU’s. (And CSU’s do give transfer preference to students from CC’s within a zone that’s local to their campuses.) Also consider USC as a transfer destination if you can get the GPA. http://www.latimes.com/local/lanow/la-me-usc-transfers-20170605-story.html
At any rate… you really could go anywhere you like, especially since you don’t seem to be price-sensitive… but the larger states like NY and CA do offer a wider range of in-state options.