I'm not sure exactly what kind of New Years experience you are looking for: whether it's an all encompasing dinner, dancing, etc, or just a nice dinner set and then bars afterwards. I was in Buenos Aires for New Years Eve as a tourist a couple of years ago and operating under similar circumstances. Though we arrived a few days beforehand with the plan to check things out around town for something suitable.

The hotels seemed, as you have found, expensive. But the celebrations there were comprehensive. (We were staying at the Park Tower btw.) We found several restaurants listing dinners with some entertainment, priced anywhere from $50 and up. Most still had availability up till right before NYE.

In the end we decided to just wing it and I think we made the right decision. We ended up at one of the very nice restaurants in Puerto Maduro. We made the reservation on the afternoon of the 31st for their dinner set which was comprehensive including drinks for, if I recall correctly, was no more than $35 per person. Screaming bargain. There was no issue securing the reservation for the 3 of us and most of the restaurants were still showing available that afternoon.

After dinner (which included midnight obviously) we strolled down to the large club at the end of the harbor (the one in the tent) and proceeded to have a fine time. There was a nominal cover charge that night even.

The night continued with a wild taxi ride with a couple of Texan gauchos (who knew Texans were buying ranches in Salta??) We ended up at some of the bars in Recoleta facing the cemetary. Touristy, but fun. The sun was well up by the time we stumbled back to the Park Tower.

Keep in mind that in the early hours of New Years Day you will NOT be able to find a cab if you wander too far from where you're staying.