I think Vassar would be a great fit. I’ve just received a full scholarship from them. Their financial aid will drastically reduce the price despite the fact that Vassar is the second most expensive college in the country (my estimated cost of attending would have been about $73,700 with fees).
You mentioned that your parents didn’t want to pay more than $20,000 a year. Although Vassar’s cost surpasses $73,000, their average financial aid is $54,665 for those who received aid. I think that the number that you get on your FAFSA is a good indicator of what you would have to pay for Vassar.(since they cover 100% of financial need)
And since my FAFSA returned with a big fat 0 for the student contribution, I have to pay, you guessed it, 0!
Here is their financial aid webpage: https://admissions.vassar.edu/financial-aid/
Vassar will also super-score your ACT. I took the ACT twice, and made a 30 and the first time and a 32 the second, but after super-scoring Vassar considered my ACT a 33.(super-scoring averages your highest sub-scores together)
And as to being close to New York, Vassar is about 70 miles north of New York City, so visiting the city is fairly easy. Internships in New York City, including journalism internships, are not uncommon as well.
(Also, Vassar’s campus is absolutely beautiful)
I hope you’ll look into applying to Vassar, I think they have a lot to offer you.