I like going to the Lychee House because it's a warm and bright environment with a very accessible menu. With a vast array of standards (chicken with broccoli, wonton soup, Peking duck, etc.) alongside an impressive vegetarian spread (you can ask for any soup or dish without meat and there's even a whole section of the menu dedicated to bean curd dishes), the Lychee House feels very upscale with its tuxedo-wearing waiters, but it's not a stuffy joint at all.
I suggest looking at the Dim Sum menu first, just to familiarize yourself with the smaller of the two menus presented to you at your table. If you'd like to peruse the standard dinner menu, be warned - it is a slightly overwhelming experience upon first glance. However, it is so well-organized (by course, by contents, and then by size) that you'll notice the ordering process is just as easy as your standard takeout order that you love. It's just presented to you with much more style.
All of the main course dishes are extremely reasonable in price ($12-20) for a midtown restaurant. The restaurant is never very crowded. You need not even call ahead for a reservation.
Overall, a very enjoyable dining experience.