Is there a place where I can sell my baseball, football and basketball cards in New York City?

Pawn shop

you can go either to eBay (keep in mind they'll pay pretty much anything) or you can go to local or regional events that are usually held at expo marts or convention centers etc. they usually have these several times a year however keep in mind you're going into the lions dens here. these people LIVE trading cards so they'll know what it's worht and make sure they pay less for it. also they are FAR more picky about condition of the cards than anyone else. There are many guides or resources that offer the cards value and such however the single most trusted (and unofficial industry standard) is the Beckett Guides. These are like the Kelly Blue Books for the card trading industry. they are sold at any local card shop or even online. they are monthly issued and are very accurate in their appraisals. they make ones for all sports including the ones mentioned above. get one of each and see the ballpark of what they're worth and then you can get an idea of what's a fair price for them. Also note that the condition of the cards is EXTREMELY important. even the slightest dog eared corner or smudge can descrease the value so be aware of that.