I was blessed to be in Buenos Aires for a total of five weeks from late April through the beginning of June this year.
It's worth taking the Buenos Aires yellow "hop-on hop-off" bus for a day. This will give you a good overview of the central parts of the city. You can then go back and see to more depth the places which you saw while on the bus.
Consider staying at an AirBnB property. You can save a lot of money by doing this AND your host can help guide you as well. There's a guy named "Mateo" and a young lady named "Catherine" who were great hosts. You'll know them if you search for properties on AirBnB.
I did not really do anything "gay". However, I did go to a club called Brook in Palermo. It was wild and did not really get started until about 1am.
I did not do anything outside of Buenos Aires. There was already too much to see and do, and I was only there for five weeks. That said, the next time I go (and I know there will be a next time soon) I will most likely go to Patagonia, Mendoza, and/or Iguazu Falls.
In addition to seeing a "Tango Show" (La Ventana), I also managed to go to a "milonga" for a genuine, community tango experience. "Milonga del Sueño Porteño" is where I went. However, there is a gay milonga called "La Marshall" (lamarshallmilonga.com.ar)
Don't bother bringing dollars or euros. Use Xoom.com to safely change your money at near the "dolar blue" rate. Changing money on the street is dangerous. Don't use credit cards, the official exchange rate is a waste of money. Only change about ARS$3500 at a time (enough for a few days to a week) because the exchange rate changes frequently, and you don't want to end up holding a lot of pesos when you leave Argentina. Sadly, there is little to no market for changing pesos back to dollars/euros without taking a huge haircut.
Pack light. Wear sportswear to blend in, and avoid wearing anything that looks too new, too expensive, and too flashy. Bring an old daypack with you because one that looks too new might peg you for robbery.
I would suggest NOT renting a car if you can help it. Public transit works well, and driving in Buenos Aires is...well..."like a tango". It moves and flows suddenly, swiftly, and dangerously. The lines on the road are merely a decoration. "Radio Taxi" is the preferred taxi service if you use taxis. Bicycling is suicide.
Also, pick up a copy of "How to Speak Argento" before you go.
Those are a few things to consider.
Aloha and Be Well!