I did a trip to Argentina last month. I went from Nov. 24 to Dec 24. I felt like it was barely enough time to experience Argentina as a whole. Ditto to the above statements by other posters.
8 to 10 days is barely enough time to experience Torres Del Paine alone. But I will try to have a go at some sort of agenda for you.
I would fly to Buenos Aires, and spend maybe a couple of days there to see some of the sites. I went alone, and felt very safe the whole time. Taxis are relatively cheap, but what is even cheaper is the highly convienient subway system, though it does get hot and crowded during rush hour around 8pm. Some of the places to see is Puerto Madero, Parque de San Martin, San Telmo for some tango dancing, and maybe if you get there on a sunday, you can go to a futbol game, which is always a great way to see the locals.
From Buenos Aires you can fly to El Calafate. I went with Aerolineas Argentinas from the Jorge Newberry Airport, (not EZE, the international airport). Prices vary of course, but it costs about $300 for a round trip. From El Calafate, you have many busing options. Once you arrive in Calafate, there is a shuttle (i forget the name), that can take you into town. Their kiosk is right before you exit to the main lobby of the airport. I believe the cost was about AR$18 or about U$S6. Don't take the U$S40 taxi, its a rip. Ask the shuttle service to take you to the Bus terminal in the center of town. In the bus terminal, there's usually a few ladies at the info desk that can speak English, (if you don't speak spanish). From this terminal, you can go to Torres Del Paine, in southern Chile, via Puerto Natales. You can also go to El Chalten which lies at the outskirts of Fitz Roy/Cerro Torre. Also, you can visit the Perito Moreno glacier via ferry which can take you to almost touching distance to the glacier. There are also some options of going to Ushaia and other far off places, but 14 hours is about my limit in travelling in a bus. My suggestion would be to travel via plane to those places if you want.
As far as my opinion on some of the places I mentioned, I found Chile to be overall expensive, and Torres del Paine and Puerto Natales to be ridiculously expensive. I believe the 2 hour bus trip from Puerto Natales was u$s30, the entrance fee another u$s35. If you wanted to stay inside the park, a tent space was u$s14 or a bed at the hostel was $44/person. A backpacking trip doing the "W" would be the only reason to go, but IMO, Yosemite is better. Fitz Roy in the Argentine Patagonia on the other hand I found to be far more reasonable. No entrance fee to the park, a u$s 14 bus trip from el Chalten. You can also stay at a hostel for u$s12. Perito Moreno is only a day trip, but definitely worth taking. I believe about u$s 30 for a bus ride and a ferry ride to the glacier.
I only spent 8 days in Patagonia, after a 3 week Aconcagua trip, and I felt hurried. IMHO, if you're going through the hassle of going all the way to Patagonia, is to find a time in your schedule to take 3 weeks, and "do it right" and get your money's worth out of it.
Argentina is generally safe. Patagonia and Mendoza regions really safe. BA has the same precautions as any big city. Taxi touts the biggest criminals, watch out for them at the airport.