Ramps over the highway are few and far between. Try Delancy Street or Cherry/Grand Street. The Grand Street ramp is the closer of the two ramps, but there is better parking under the Williamsburg Bridge, which is the Delancy Street ramp.
By Subway, take the F train to Delancey, walk South to Grand Street and east to the fields or
By Subway: F to Delancy Street; L to First Avenue; J, M, or Z to Delancy/Essex.
By car, take the FDR South, exit Grand Street, fields are on your left.
Detailed Map of the East River Park
Area