Both New York and California are both members of the Drivers License Compact (DLC). This Compact requires member states to report tickets received by motorist back to the state where they received a license to drive. The state that the driver is licensed in, in your case New York, then determines if they will add the violation to the person's driving record and assign other penalties or points.
The New York State Department of Motor Vehicles has decided that except for citations from Ontario and Quebec, points are not added to your NYS driver record if you commit an out of state traffic violation. The New York DMV also does not record out of state violations onto your driver's history.
To find out the cost of your speeding ticket you will need to check with the California court from the county in which you received the citation since amounts can vary by jurisdiction. You can either call the court, there should be a phone number to call, or go online since many CA county courts now let you look up your citation online and pay it.
If you do not pay this out of state ticket, New York would likely take action against your NYS license. New York takes part in the Non-Resident Violator Compact which requires member states to suspend the drivers license of those who get traffic tickets for moving violations in other states and fail to pay them.
So in order to not hurt your NYS driving record with a suspension due to failure to pay a ticket, it would be better to take care of the California ticket.