On the Argentina side its staying at El Calafete and visiting the Los Glaciares NP, primarily the Perito Moreno glacier definitely going to El Chalten and hiking the park around Fitz Roy and El Torre. There's also Viedma Glacier there if you want to strap on crampons and walk the glacier.
In Chile the main place to stay is at Lake Pehoe and work the Torres Del Paine NP.
We went in 2nd half of April - the very end of the season. We were literally the last party at our hotel in El Chalten. The colors were intense and the weather can swing hard. The 2 parties before us never saw the mountains from El Chalten. We saw them every day. Temps ranged from 15-60. Winds ranged from 20-80 mph! We had 2 days were 60-80 mph gusts were a challenge on glass, tripods, packs and long exposures. I even had one lens that would flex about 2-3 pixels on my camera body. Small lakes would turn into rough seas! You can see the winds vaporizing the water in these pics.
Dave
Dave these shots are absolutely spectacular. It must have been a real challenge in the weather that you describe.
Michael
MD 35-70 Macro on A7.
Had to do a B/W conversion to balance the different intensities (mid-day light) and to deal with the color cast from the canopy. I should make a habit of carrying a polariser.
Yesterday there were a lot of street concerts in Stockholm and the weather was amazing. Loads of people on the street and crazy good artists, from young kids to old dudes.