Cheapest is by Airtrain/subway ($7.25); the 40th St. and 33rd St. stations on the #7 subway are closest to the Sunnyside area but you would still have to walk quite a bit. Take Airtrain from your terminal to Jamaica Station, transfer to the E subway, get off at Jackson Heights/Roosevelt Ave. and transfer to the inbound #7 train to either 40th St/Lowery St. or 33rd St/Rawson Ave.
Cheapest is by