By Mandarin I presume you're using the old time term for non-Cantonese restaurants. Since the Chinatown community is almost exclusively Cantonese/Toishanese and Vietnamese, any of the non-Cantonese restaurants are really interlopers and primarily tourist driven. This would include Yang Chow, Mandarin Chateau, Plum Tree and Chinese Friends. I wouldn't be caught dead in any of them. If you must go, Plum Tree is the most nicely decorated, Yang Chow is the most popular and Mandarin Chateau has the most authentic menu, so I'd probably choose that one.
You're almost certainly looking for someplace like Mandarin Chateau. The menu is all over the map, but you probably want to concentrate on the old-fashioned Shanghai-style dishes: lion's head, braised fish tail, fried rice-cake noodles, shredded bean curd, pork with salted vegetable, etc.
Mandarin is a language, no? If you're just looking for a good Chinese restaurant, here's one recent thread: http://chowhound.chow.com/topics/770796
Let us know what type of food - generic "American" Chinese, something more regional, dim sum or bbq, your various food issues, hole-in-the-wall or not, etc. It's *very* easy to be disappointed in Chinatown (like, being a vegetarian out for dim sum), but it's also possible to have an outstanding meal. But, just know that no restaurant does everything well - most places have just one or two types of foods/cuisines they can pull off, despite the size of those long menus.