I'll be in Argentina for just 10 days mid October 2015, flying into Buenos Aires. In general, I'm interested in any "must see" recommendations.
Specifically I'm interested in...
1). Whether the Iguazu falls are worth the hype and any tour operator recommendations for flight/hotel or hostel packages there.
2). Any highly recommended 1-2 day trips outside of Buenos Aires?
3). Thoughts on Uruguay and best mode of transportation there?
Iguazú Falls is pretty good - I didn't do a tour just booked flights and a hotel online. The Aerolineas Argentina site is do-able, although from memory you may need bit of Spanish for the domestic flights. The flights leave from Pistarini airport which is much closer to town than the international. For me I preferred Perito Moreno Glacier but it is further away if you are on a time limit. It is spectacular - you would need flights to El Calafate. The other great place - especially if you are going in winter - is Saltaand the environs - great. It's a difficult call - Iguazu is one of those places you need to see, but not necessarily the greatest in hindsight.
In resect to Uruguay I would go on the ferry from Buenos Aires to Colonia (Uguguay) and carry on from there on the bus if you are going further. Uruguay is good if you want countryside and it is a bit less "manic" than Argentina but more expensive and not quite as fun. Book it online or a few days in advance when you are there; the prices vary hugely and on the day it is expensive. Sign up now and you will get their specials by email.
In Buenos Aires - I'd just hang out - you will be up LATE so may need to chill in the day, shopping in Palermo, looking at the market/sights in San Telmo head out to the touristy La Boca and try lots of cafes and wander around. Also look at the Time Out - there is an English version and see what is on, there is a great arts scene in Buenos Aires and some amazing events. Enjoy.
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Christine gave you very good advices.
To go to Iguazú there are many agencies, if you want to book a package, I went with Lantours form Lan airline, but you can also buy your flight with Aerolineas or Lan and book a hotel through Booking, for example.
You can also try despegar.com to book packages, flights, hotels and more all over the country.
El Calafate is simply amazing, you can do that in 3 days too.
And to go to Uruguay definitely take a boat, Buquebus is our favorite but you also have Ferrylineas and Colonia Express. They offer trips to Colonia (Uguguay) or Montevideo with bus conexions to Montevideo, from Colonia, or to Punta del Este from both cities.
Best of luck
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