Along the Yellow River
The Yellow River is not tame. Only parts of it are navigable; other sections have quite a rapid current. Over the centuries the river has changed its course several times; the last change in 1853 moved the mouth the length of Shandong province; before then, it was well South of Qingdao. It has had many disastrous floods; irrigation and flood control projects have been going on in the area for several thousand years and have never achieved complete success.
Chinese civilization first developed along the Yellow River (Huang He). From there it spread, first to other fertile areas like the lower Yangtze (Chang Jiang) basin and the Sichuan basin further up that river, then to other zones.
The river rises in Qinghai in the foothills of the Himalayas and runs north to Inner Mongolia. There it runs in a big arc, with the Great Wall following it for some distance, before turning east toward the sea.
Cities on its route, listed from source to coast:
Of course there are many smaller towns as well.
Much of the area is not touristy. If you do not speak Chinese, you will need a least a phrasebook, preferably a bilingual guide. If possible, learn some Chinese before setting out.
 Get in
There are trains throughout the area. All the trains to western China (Xinjiang, Qinghai, Gansu) go through Lanzhou, which lies on the banks of the Yellow River. The Beijing-Lanzhou "north route" follows the Yellow River for half of its way. The train from Beijing to Tibet via Qinghai passes through several of the cities along the river. There are also boats along some parts of the river.
However, for flexibility if you want to follow the Yellow River, you would need to travel largely by road. Rich travelers might rent a car and driver, see Driving in China. Others would use buses, varied perhaps with train or boat for some sections.
 Stay safe
 Get out
From the inland end of this route, you could turn west onto the Silk Road (Lanzhou is on the main route), turn southeast to reach Xian, or go a little west to Golmud which is a jumping off point for Tibet.