I have not used this lot, but have had it recommended to me. Go over the Queensboro Bridge (59th St) from Manhattan to Queens. After you leave the bridge, take the first exit to the right into Queensboro Plaza. There should be a parking garage immediately on your right. The cost is $10/day and the garage is patrolled. Additionally, there is a subway entry next to the street entrance garage. You can connect there to several subway lines into Manhattan.