Well, that's a tough question, and conflicting reports from various newspapers don't help that inquiry. The end of this March 5th article in the New York Daily News, which focused on the deplorable conditions at Aqueduct, reports "NYRA officials did say Wednesday that there will be no admission price increase at Belmont and Saratoga this year....". A Times Union article from the same day, however, reports that "Kay also confirmed that entrance and seating prices are planned to rise. Admission prices at Belmont Park and Saratoga Race Course will be formally announced soon, based on a report supporting such increases from a consulting firm’s market research."
My guess is that reserved seating prices in Saratoga Race Course's grandstand and clubhouse will rise, but general admission prices for most days will stay the same. If I am correct, I see a rise in seating prices as short-sighted because NYRA can't sell the seats it currently has. Other than Travers Day and perhaps one or two other days featuring major stakes races, I often see hundreds of empty seats. During the weekday it seems as if 90% of the grandstand and more than half of the clubhouse seats are empty.
Perhaps general admission prices for the Travers will rise; NYRA could double the admission price for the Travers and I think it would be justified. Of course I've been to the Kentucky Derby twice now and I spent a fortune for a crappy seat last year, so I am viewing Travers prices from that perspective.
In any event I am assuming NYRA will announce seating prices very soon - they are missing out on a lot of money coming in. In previous years you had to get your reserved seating requests in by December. Now it appears you will have until April to get them in. Keep an eye on the NYRA site's Saratoga ticket/seating page for updates.