It depends upon which route you take, Exit 22 is off the Southern State Parkway, whereas Exit 31 is on the Grand Central Parkway. Both take you to the Meadowbrook, but the GCP gets you onto the Meadowbrook near Garden City, which is a bit north of where the Southern State meets the Meadowbrook.
So, if you were to take the Clearview Expressway from the Throgs Neck Bridge to the Grand Central, you would merge onto the Meadowbrook via Exit 31 on the GCP. Then, follow the Meadowbrook to Jones Beach where it turns into Ocean Parkway.
Alternatively, if you take the Clearview to the Grand Central and then merge onto the Cross Island, you would follow the Cross Island to the Southern State Parkway east which is a left lane exit. Then, you would follow the Southern State to the Meadowbrook and merge onto the Meadowbrook via Exit 22 on the SSP. Then, follow the Meadowbrook to Jones Beach.
Have fun whichever route you take!