Chat N' Chew off Union Square has fine strings - they are lightly salted and seasoned, which contrasts with the sweet onions. It's a big plate though - and as I've learned, they simply can't be reheated/recrisped in an oven. :(
Surprisingly, Virgil's (off Times Square) has excellent thin, crisp onion rings, served with blue cheese dressing. If you don't care for their Q, just sit at the bar and have an Anchor Steam draft with an order or two of onion rings.