Spa Newbie seeks NYC day trip advice

[greedyway]

Will be in NYC from 7/27 to 8/5 and have never been to Saratoga. I would like to get thoughts from experienced derby trailers on how to do a day trip.

I will not have access to a car but could rent one if that is the best way to get there. Are there easy rail/public transport options?

Aside from Carolina BBQ, what are the must-sees/must-dos for a one-day visit in Saratoga?

What day of the week is the best to go to?

Any other thoughts?

Thanks!