Neither dance nor marketing lead to well paid positions so go with the cheaper (SUNY?) College.
How much does the current private college cost? Did your parents take loans?
How much would COA/cost of attendance be at the public college?
If you don’t want to live at home, could you share an apartment near the public college? I bet it’d still be cheaper than your private college.
And beside that one public college near your home, all other public colleges in the state should be in play when you’re considering transfer.
SUNYs are well respected in NYS and should not hold you back.
What’s your current GPA?
Btw you don’t have to limit yourself to just one SUNY, you can apply to several SUNYs and see which ones would admit you. Purchase is known for its arts programs so if you apply for a business major/dance minor you’d get excellent instruction for instance.
Do you have an internship lined up for this summer (hopefully, paid)? If not, it’s quite late to be looking, but go to the career center immediately and make your expensive private college alumni network work for you one last time. 
Go on Handshake, etc.
Someone upthread mentioned that the next 2-3 years may be the last time you can actively pursue your passion for dance.
You could pursue dance as a minor at a SUNY and make sure you strengthen your major (marketing currently has very low ROI so you need to add to it so that you make good money with it to pay back your federal loans - hoping you didn’t take more than the 5.5k federal loans - AND have money on the side to continue dance on weekends.)
To make your marketing major work for you, you’ll need solid statistics&data science classes (to highlight on your resume under “relevant courses” since you won’t have a minor). Others will chime in as to other ways to make your Marketing major stronger.
Or you could switch out of Marketing - Supply Chain is always hiring&in need of good candidates.