Peru
Use taxis to get you to the start of hikes. Ask the driver and get them to drop you at the top of the pass out of the valley and walk back down through the fields.
Alternatively, they'll take you up to the start of the hikes (see travel guides) and will wait for you as long as it takes until you come back down again. Take food and water, we gave our driver some too - and don't pay until you get back. All for a few dollars.
You can also catch collectivos - we did that but had to hitch back down from a one-day hike on a tour bus full of happy Peruvians who'd been on a day trip up into the lakes.
Follow in the footsteps of Joe 'Touching the Void' Simpson and trek around this stunning, remote mountain range. Although you may want to avoid the near-death crawl across a glacier.
Quite challenging walking circuit (10-14 days), over 5,000 metres at one point, with the most amazing mountain views you will ever see. Don't miss the natural hotspring where you can soak weary limbs surrounded by a cirque of spiky peaks about half way round the circuit.
There are loads of trekking agencies in Huaraz where you can hire tent, stove, food and a donkey to carry it all for you!
If you haven't got time for the Huayhuash circuit, this is a great trek with spectacular scenery. We went with Huascaran Adventure Travel - great guide and much better food and kit than some rival operators. We booked through the Albergue Churup in Huaraz, which was a good place to stay.
A two-week trek run out of Huaraz, taking in epically beautiful scenery: alpine valleys, glacial lakes, snow capped mountains. See where Joe Simpson "touched the void", from the comfort of a valley-floor campsite, but be prepared for long days and thin air.
Most of the local agencies along the main street running to the Plaza offer trips, as do KE Adventure Travel, Journey Latin America etc if you're time pressed and need to organise before you get there.
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