I have one great place for you to try. Nice ambiance, very different. Yaffa's Tea Room, on Harrison and Greenwich. They have a tea list and a great little menu at reasonable prices. Everything smells great. Go there and relax after a long day and just hang out with some odd french music in the background!
This may not fit your criteria, but when I'm in the Wall Street or South Street Area I hit Jeremy's Ale House on either Coentes or Water Slip (I don't have the address handy.) Tap beer served in 32 oz buckets, fried clams, calamari, shrimp in a place that has all the ambience of a big tool shed. But it's the favorite of blue collar and white collar alike. Come to think of it, I haven't been in several years. I hope it's still there, and just as greasy. Good luck.