Congratulations! You briefly mentioned the cost of living, but you didn't mention tuition. Are you paying for your own tuition?
Something you didn't mention is that Stony Brook is ranked 58 on US World News (Research), whereas SUNY Downstate is unranked. However, the rankings aren't everything, and you have to consider things like fit, location, cost, opportunities for your specialty(ies) of interest, etc. Rank certainly shouldn't dictate your decision, but this is just one of many factors to think about!
With regards to your interest in derm, I actually do know a few residents and attendings who went to both Stony Brook and SUNY Downstate. None of them had any issues. Both are well-respected, accredited MD programs that have more than enough opportunities you'll need to get into any specialty. At the end of the day, it does come down to your work ethic!
Ultimately, I personally would highly recommend following the money if there's a huge difference.
Both are great MD programs. Based on the information I have so far, you really can't go wrong. If you provide more information like the cost differential, where you grew up and where you'd like to practice, what you want out of a curriculum (like a research block, which maybe only one school will have), etc.. then it would be much easier to advise you haha. I'll check back here if you do provide more info
I know this is a lot, but congratulations. You can't go wrong! Best of luck!