In reply to robs123:
Most commercially guided trips are, by nature, on pretty easy routes and it's a good idea to aim for a tech level well below what you climb in the Alps, as altitude, illness, time, lack of will etc all intervene to make things tougher.
If you don't like crowds, stay off the main Khumbu peaks of Imja Tse, Lobuje and Mera. But companies do guide Cholatse SW ridge (now a Trekking Peak but not easy), Kyajo Ri (popular but not often summited) or Nirekha, so maybe google for them.
In the Indian Himalaya the most popular 6K is Stok Kangri near Leh, but it is very easy and often crowded. Ladakh has some other peaks easily organised but they are non-technical. Kang Yatse / Kang Yissay, often has its lower summit KYII guided, but it is nothing really, though an ascent of KY proper, via the east side, would be a good climb easily organised, and there are nice easy peaks nearby. In other parts of Himachal local companies will guide peaks like CB13, Indrasan or Menthosa but you'd need a partner really.