I want to go on holiday, but not to the normal holiday destinations, instead to a destination, which is quite remote, new and has very few tourists. Most of the places which I have read about on the internet are quite far away and to be honest I don't want to make such a long trip. Leh seems like a good place, but I do not know how popular it is. For the holiday it would be just me and my wife, so it is not necessary that there has to be any facilities like shops nears by.
Munsiyari is a good destination to go to, but the only issue is the distance. If you want two different destinations then you can make a halt at Almora which is a lovely place to visit as well, not crowded and has beautiful views. Leh is not a crowded place so you can consider that as well.
Leh is a beautiful place and it is not crowded either, I think it should be the first choice for your holiday destination as it is must see place. Lansdowne is also a beautiful place to visit, it does have some crowd but not a lot. Prits has mentioned Almora is another place which you visit, there is not much to do around the area and instead I would like to suggest Binsar which is slightly further ahead of Almora. There are many resorts there and a lot of activites which are conducted by the resorts.
I came across a thread on the forum about less known destinations in North India, thought it would be useful for the original posters query.
You should visit Spiti, it is known but not a crowded place at all, something of your liking and requirement.
I have heard of Munsiyari, Almora and Binsar but these are slightly too far, I would consider them if I plan a long distance holiday. On the other hand Spiti does seem more appealing, I can not recall but other places of visit near by are Shojha and Kaza which I have read about in the thread lesser known places in North India.
It is around 800km, which quite far, but worth it for the remote holiday destination which you are looking for.