I had my 40th bday dinner at Altitude 95 (the restaurant on the 2nd level of the Eiffel Tower). This was many (ahem!) years ago – I had to book the reservation via fax! I had mentioned that it was for a special birthday when making the reservation, but did not mention this once we were there. At then end of dinner they brought out a lovely bit of cake with a candle. It was an interesting atmosphere and we had (requested) a window table. Great memory. I do know that it has undergone renovation since then, so I really don’t know what it is like now. It was not expensive in the way Jules Verne (the other restaurant in the ET) is. Perhaps somebody else has more up-to-date info.
There is also the option of a dinner cruise. I had read recently about one that actually has decent food (most of them don’t). http://www.calife.com/ For a special occasion, I don’t think it is a bank-breaker at 67 Euro each (not including drinks). It has great reviews. I did a dinner cruise (not this one) with my mother many years ago and she just loved it.
I have also had a special dinner at Le Train Bleu. Personally I didn't love the food and felt it was rather pricey, the service was without personality (obviously could have been just our waiter, but very formal), but the atmosphere was amazing.
Have a wonderful time!