We travelled to Torres del Paine this February and I spent hours trying to research a good route for the trek, how many nights to spend at each hostel and whether you can get straight to the park from El Calafate as I didn't have enough days to spend a night in Chile before starting the trek. I have been meaning to write this post for ages as hopefully it might help people in the same situation as I was.
Firstly, yes you can get from El Calafate to the start of the trek in the same day. Always Glaciers runs a day trip to the park from El Calafate, and will take you with the other people on the trip and drop you off at guarderia laguna amarga after lunch. You make a few other stops on the way where, if its clear, you get a great view of the peaks from afar. After they drop you off you will have enough time to walk to the las torres hostel, or you can catch one of the mini buses, there were lots when we got off the bus waiting to take people.
When you book the tour you arrange which day you want to be collected and they pick you up from the same point and take you back to El Calafate. The trip is quite expensive and its a long way but if, like us, you don't have a lot of time its a pretty efficient way to get there. Just to note you can't take any fresh food with you over the border and there is only one shop after the border crossing that sells food and is quite expensive. We didn't take anything because we went fully catered at the hostels.
To book this you have to contact Always Glaciers directly as I don't think its something they normally offer.
Once in the park my recommended itinerary for a 5 night trip would be:
Spend the first night at Las Torres
First day climb to the Torres and return to the hostel for a second night - this way you don't need to carry all your kit.
Second day walk to Los Cuernos and spend the night there - this walk doesn't take all day so you don't have to rush.
Third day, walk to camp italiano and leave you big bags there (this campsite was revolting when we were there so I recommend taking a bin bag or simialr to wrap your rucksack in as there was open sewerage and rats when we were there.
From the camp walk up the valley to the top, then walk back down, collect you bag from the campsite and walk on to refuge paine grande. This is a long day but you can do it, the end section is really flat and the hostel at the end is the nicest one with a bar and lovely outside seating so a good reward at the end of a long day.
The next day I would walk from here up to Glacier Grey, turn around and return to Grande Paine for a second night.
This isn't what we did but in hindsight it would have been a much better plan, partly because the hostel at Refugio Grey isn't anything like as nice as the one at Paine Grande and also because I thought we would have time to catch the ferry back across Lago Grey the next day but we didn't and had to rush back to Paine Grande in the morning.
By staying the night at Paine Grande you would be able to relax in the morning, catch the boat across to Guareria Pudeto and from there you can get a bus back to the park entrance in plenty of time for the Always Glacier bus to collect you and take you back to El Calafate. You don't need to book this bus as there are several waiting to meet the boat when it gets in.
The hostels were warm and welcoming and the lunches provided were plenty of fuel for the long days of walking, we certinaly didn't need any extra food,
In El Calafate I can highly recommend the Miziyato Inn as they were just lovely and also helped us book car hire and the Big Ice trip in advance.
We also spent 2 nights in El Chalten, we hired a car in El Calafate and drove across. The weather when we were there was pretty awful and in the end we spent a lot of time in the microbrewery playing scrabble and eating waffles! What small bit of the mountain we did see looked very impressive, but in comparison to Torres Del Paine the park didn't have as much variety, nor the sense of achivement of having to work hard to get to see the great views, so if I could only have done one I would go for TDP every time, but like I said we didn't exactly have the best weather in El Chalten. Puerto Merino was also unmissable.
Hope someone finds this helpful and have a great trip!