Don't quite know why anyone would want to fly out of Buenos Aires, because that is one neat place, and so exciting and hard to beat. Everything is right there. And, that's the only place I've been in regards to your other two places, (Chile and Patagonia). We stayed at the Wilton Hotel. (Buenos Aires Wilton Hotel (Buenos Aires, Argentina) | Expedia). We walked all over Buenos Aires, lots of nearby shops and cafe's. I can't express how great the food there is. They've got the best EMPANADAS in the world I think. Pastry shops all over the place, pizza joints, steak joints, wine joints. I know air fare is quite pricey within Argentina, and we had no deals with their airlines when I checked. It was like 400 bucks each way per person from Buenos Aires to Mendoza when I checked. No interline agreements with our airlines and theirs either. Chile turned me off with their 100 dollar enterance fee plus departure fee. Sort of like going to Beijing. And fares from Santiago to B.A. was ridiculous within those local airlines with no interline agreements. Maybe all that is different now, but not when I went around 7 years ago or so.