You might find it useful to go to OpenStreetmap and zoom to your area of interest, then use the query tool (the Question Mark icon). You don't need to be logged in to use this.
Next, click on or near the water feature you want to examine - a list of candidates will appear on a panel in the left.
You should hopefully be able to find the feature, and click on the link - this should show how the feature has been tagged.
In most cases, rivers should be tagged 'waterway', but it's possible some may have been tagged with something else, like 'natural'
Also - I'm assuming you're using QuickOSM plugin, as you tagged this QGIS? If so, check the 'advanced' settings in query, and make sure you have all types of geometry selected. Some rivers are lines, but more complex rivers (wide rivers with islands for example) can be relations or multipolygons.
Note that if you leave the value blank, it matches any value for waterway - you don't have to search for canals and streams separately unless you want them in separate layers.
Best Answer
When there is a boundary relation for that city area (like political boundaries) you can use its name for a query via overpass-api or overpass-turbo.
So first find out about any good boundary relation within the OSM data: go to http://nominatim.openstreetmap.org and try to find a boundary relation for your city ... for example type "Buxtehude" in its search box there (Buxtehude is a small city in the north of Germany) ... see the results and its detail links.
With that background knowledge vidit http://overpass-turbo.eu and use its wizard modus: Try "shop=* in Buxtehude" there ... without ""
Thus you can limit any query via overpass-api or overpass-turbo (or even QuickOSM-Plugin in QGIS) to any city area as long as we have boundaries for that in the OSM data.
Please refer to the documentation of overpass-api and overpass turbo at wiki.osm.org
If you get stuck about a boundary is present or not, tell us the name of the city we can use for testing purposes.
Tell us here about success or failure in general.