Lives up to its difficulty level. There are also some rivers in Australia and the Nordic countries that flow by major cities, which would be fun to see.
I wouldn't say Xi'an lies on the Yellow River. It's a good 120km off, judging from Google Maps. I'd say that the Wei River should be the correct answer, or at least an accepted type-in.
Yeah, Xi'an is clearly not on the Yellow River. A good fix without an excessive increase in difficulty would probably be to replace Xi'an with Lanzhou, which is still a fairly significant Chinese city that is right on the banks of the Yellow River.
The same way the Willamette and Columbia are counted for Portland, the first flowing into the second, it would be consistent to count the Saône as well as the Rhône river for Lyon. The Saône is one of the longest bodies of water in France.
If you're going to accept multiple rivers for one city may I suggest you also allow the Saône for Lyon as this is a very famous river in France (2 départements are named after it) and Lyon is known as the confluence of these rivers. Alternatively, maybe change the city to somewhere like Avignon or Geneva?
I only know Yuma because I live in the state.