I spent 4 days in Torres del Paine... IMO due to variable weather you need at LEAST that many days. If photography is the main point, you'd do well to spend a full week down there to improve your chances of getting a couple good sunrises or sunsets.
Anyway... we stayed at Hosteria Los Torres. A nice place... very expensive for Chile (anything down there is), but it had a restaurant. There are few lodging options in the park. Hosteria was like $200 US/night (probably more now). Anyway... out the back of the Hosteria it was maybe 4 miles up to a lake at the base of the Torres.
You'll see lots of guanacos:
And here's the view of the Torres from the top of the hike (I actually made this hike... about 4 miles each way... 2 days in a row because on the first day I couldn't see the back of the lake at all and it was raining hard all day):
Behind the Torres (from the other side) are the Cuernos del Paine:
And if you're lucky you might get a decent picture of a Condor:
This was more of a "snapshot" trip with the girlfriend (now wife) so most are in crappy mid-day light but it's a beautiful area. But the weather down there, again, is unpredictable, so don't plan on getting good weather everywhere if you chug along on the itinerary.
Anyway, the Hosteria itself is very centrally located to the Torres and the Cuernos. From what I recall much of the rest of the park was camping only. It's not all that well travelled down there -- and few of the folks are Chilean (or Argentinean). Most of them are European.
Punta Arenas itself is small (and windy!) and maybe worth a day or two but nothing huge. There is a breeding colony of Magellanic penguins about 30 KM outside the city if you're into that. Oh, and note that much of the transportation from Punta Arenas to Torres del Paine is small shuttles that will stop by Guanaco and Ostrich farms on the way to the park... No doubt they're paid by the farmers to bring people buy to buy stuff.
I didn't get to El Calafate or El Chalten... just into Torres del Paine for 4 days before heading up to the lake region.