Bruno_Tibet wrote: Basically every mountain west of Dhaulagiri. This includes Kanjiroba (6883m, Lat 29°22'33" Lon 82°38'15") in Dolpa, several high 6000ers further west on the Nepal-Tibet border (don't know if these peaks are open from Nepal), and the far west peaks around Saipal (7035m, Lat 29°53'21" Lon 81°29'39") and Api (7132m, Lat 30°00'18" Lon 80°55'42").
There's some really interesting stuff, and lots of empty boring hills in-between too
There are unclimbed peaks that are on the permitted list (eg. Dhaulasiri looks good) and stuff on the border you can't go to - though the Japanese and Brits have been getting into some interesting places the last year or two there.
The real problem is the access. You might save on the peak fee but spend more on flights and porters. Even Putha Hiunchuli, 'free' under this system, and a popular and easy 7000er, takes either a long trek, with no tea-houses, or two plane flights and a short trek. If you take those two flights, how does all your food and gear for a four-week trip get in there? You need a good agent to organise that porter circus!
The Poles and others did quite a bit around Api and Saipal many years ago - originally coming in from India - and several British and Japanese expeditions explored the Kanjiroba area. Other more recent expeditions have found troubles getting up some of these valleys, then finding the right peak. You need time and a lot of patience, even before you set foot on the mountain. Finding guides/sirdars and porters both capable and willing to do these kinds of trips is getting harder as time goes by. More of them want easy trekking or commercial peak jobs, or city jobs. Fewer people live in the country, so fewer people know how to get to anything not in a company brochure.