For wonderful, authentic Spanish food (especially the seafood paella), and incredible Sangria, try Sevilla Restaurant & Bar in the Village (Greenwich Village): 62 Charles Street (Corner 4th Street). As far as I know, they don't take reservations, so do your best to be at the door by 6pm on a weekend night (probably later on a week night).
I've lost count how many times we've had dinner there, and we've brought friends to Sevilla from Connecticut, California (SF and LA) and NYC. The food has always been consistently great and there's always a line out the door by the time we leave (on weekends, anyway).
Sevilla has a nice Old World/neighborhood feel to it... not "touristy" at all. The atmosphere is cozy and intimate, but once it fills up, can be fairly cacophonous (in a fun way). The aproned all-male waitstaff keep things moving along efficiently. Oh, and the prices are pretty reasonable, too.