I have been searching for high mountains which I can ascend without ropes, but probably with ice axe and crampons, but unguided unportered (probably) wild camping and with the minimum of fuss, visas and red tape. Cheap to be there also being and advantage. I have liked The Pyrenees, The Atlas mountains, Parts of Peru (the Salcantay trail) and of course The Scottish Highlands.
The Himalayas seem to require visas and being part of a tour almost everywhere. I know Kelvin was just in Iran which was not easy on visas but sounded red tape free after that. The north American mountains Denali and such sound very busy and need visas I think. Kilimanjaro is overloaded and difficult to do freely although Mt Kenya sounds better. All in all South America seems to suit what I am looking for best. Aconcagua needs permits but off season they are not so bad, perhaps avoid Aconcagua.
Has anyone been to the 5-7000m mountains of the Andes and could point me in good directions or does anyone know of another place that fits my criteria?
Do you feel the need for height and snow capped peaks?
I've been into the Cordeilla Blanca myself but only trekking, likewise further south down the Andes. Surely there will be some trekking / climbing books on S America, the tourist agencies in the UK may help you, Google might, what of the climbing community and magazines, that's more your starting point isn't it?
A friend of mine did a couple of 6,000m tops out of Huaraz. Not technical and not too difficult if I remember correctly, although she did go with a local guide (arranged from Caroline Guest House).
The Andes: A Trekking Guide and The Andes: A Guide for Climbers are both excellent books by Scottish guy called John Biggar. He's a really nice chap and knows the Andes probably better than anyone else in the UK. He's happy to give you advice and information too.
There is an interesting list of Peaks in the Cordillera Blanca here. I seem to remember reading somewhere that Huascaran National Park has some pretty restrictive regulations requiring that all foreigners hire guides and donkeys for both trekking and mountaineering - not sure if they apply just to the Park (and so the Cordillera Blanca), or cover the whole of Peru. Well worth following Mr Sargeants advice, and contacting John Biggar to ask about this.
Both India and Nepal require a Visa, but they're not hard to obtain. Some areas in the Himalaya in both countries also require permits, mostly if they lie close to a border. But not as many as you might think - there is still lots of scope for independent trekking. India relaxed its mountaineering rules somewhat a few years back (see here and here), creating a class of "Open Peaks" which while they still need a permit (and peak fee) can be easily arranged through the IMF here. They also list 3 "Trekking Peaks" which are completely free of any permit requirements or peak fees (see links on the IMF website).