Hi, Mr Mohammed. To sample culture of China, I would say you picked the right places. As to the Lijiang problems, I think Kunming can not be avoid, at least you should go through it once. There are direct flight to Lijiang from Beijing, Shanghai and Hangzhou, but you still have to go to Guilin via Kunming. If you want to srop a city to add Lijiang, I suggest Hohhot. April is not the very good time to see desert or grassland and comparatively, Lijiang is more attractive. I suggest you stay nearby Nanjing Road/People's Square in Shanghai, Wangfujing/Xidan/Qianmen area in Beijing, within the City Wall in Xian (closer to Bell/Drum Tower and Xi'an Moslem Street(https://www.travelchinaguide.com/attraction/shaanxi/xian/moslem-street.htm) ), close to east bank of West Lake in Hangzhou. The city proper of Lijiang and Guilin are not big. My understanding on a budget hotel is like a chain express hotel, like Jinjiang Inn or Home Inn. Compared to star hotels, they usually have more convenient location and the hotel condition is not bad. Personally, I prefer Jinjiang Inn. I once lived in the Jinjiang Inn in Qianmen, Beijing.Muslim food is easy to find in Beijing and Xian. The Ox Street in Beijing and Moslem Street in Xian are Muslim communities. You can travel alone in most of those cities alone, but I think you need English guide while visiting attractions in Beijing, Xian, Lijiang. If you want to do more free traveling, I think you need book tours at least at Xian and Beijing. China tours(https://www.travelchinaguide.com/tour/default.htm) for reference here. Fine one and arrange your tours in advance. It saves time and they can arrange pick-up hotels, train or flight tickets ready.

Dear Mr. Qi,
Thanks a lot for the information. I will definately take into account your suggestions. Possibly I will drop Hohot in favour of Lijiang.
Grateful for your valuable advice
Mohammed