Originally Posted by wahooflyer

Better yet, if you're really on a budget, just about every residential street on the Upper East Side, from 65th all the way up to 96th, has free parking. Find a spot here and then take the Lexington Avenue (no. 4, 5, 6) subway down to Grand Central.

There are street cleaning restrictions, however---one side of the street is restricted for an hour and a half on Mondays and Thursdays, and the other side is no parking for an hour and a half on Tuesdays and Fridays. Wednesday is always the "free" day in Manhattan with no alternate-side rules in effect. Be sure to read the signs, or otherwise you'll get an $85 ticket if you don't move your car during street cleaning.

If you don't want to go with this option, though the parking lots over on the far West Side, that dhammer53 mentioned, are going to be the cheapest within a reasonable distance. You might be able to find cheaper garage or lot parking in Chelsea (west 20s) but that's a much longer walk or subway ride to Grand Central.