Hey- I'd say anywhere quiet, small and dark. Most of the restaurants here have the same food, so that really isn't a big deal. It's all about atmosphere. A lot of people like going to puerto madero, which isn't bad, but you usually pay more than you really should. you can get equally good food in a number of places, including calle chile in san telmo or calle san martin in retiro/microcentro. Good luck, and don't forget to top it all off with a good malbec!
I actually went on a date to Gardiner, it´s located in Costanera Norte. They have a great outdoor patio and it faces the river, great on a cool summer/autumn night. The place is not cheap but very romantic if you sit outside. Have fun!
Romantic dinner without spending too much? I suggest you bring her to your flat, which you have cleaned up and decorated with flowers, and cook something nice for her. Candles and wine, of course. Hard to get more romantic than having a man cook a really nice dinner for you.
I reccomend Carnal in Palermo Viejo. It's on Niceto Viega right across from Niceto boliche. It's small, but has an amazing terrace, a good drinks menu and I hear the food is good (only been there for drinks). Otherwise, Olsen is fun (and delicious) is you like a minimalist aesthetic and Scandinavian food.