Since you mention Italian try:

Pepolino - absolutely first rate - in Tribeca

I Trulli - cuisine of Puglia (where we rented a house last year) - a superb cuisine.

Chinese - generally speaking - is not really for a special celebration -- service is not geared for that sort of thing.

But if you want to slightly splurge: Chanterelle - and tell them it's your birthday. You will be treated royally.

Decent steak houses are very expensive and you're just paying for that high priced cut of meat.

And Tex-mex? No es para celebrar una ocasion. Ok para un taco - corriendo. (not for celebrating an occasion. OK for a taco - on the run).