I did the abbreviated three day loop in Cerro Castillo National Reserve, starting and ending in town. Longer versions of the hike would require hitchhiking
The west side near Laguna Duff is worth visiting and has better campsites for windy days
There is an information booth at the trailhead near town where you can register and pay to enter the reserve (very cheap around $3 USD in 2016)
I visited Parque Patagonia during its first summer open to the public (2015-2016). It was not very crowded, most of the people at the campsite were volunteers for Conservacion Patagonia.
I did dayhikes on the Lagunas Altas trail, the Aviles Valley, and to the Rio Baker Confluence
A longer backpack could be done in the Aviles Valley to the Jeinemeni mountain range, which looks excellent from the short dayhike into the region.
It takes about 7 hours on the Carretera Austral Highway to reach Parque Patagonia from the Balmaceda Airport (170 miles). There are gas stations in Coyhaique, Puerto Rio Tranquilo, and Cochrane. I had a good experience with Traeger Rental Car.
Resources: LP Trekking in Patagonia Andes (good details on Cerro Castillo), Patagonia Park map