The type of home you are looking for and the price point determine where along the river you will find homes available. There are condos available downtown within a block of the river. There are also single family homes available along the river but not located downtown. Try doing a search for homes in 89501 (downtown Reno). Hope this helps! Tiffany Bacon, Keller Williams Group One, Inc.
There are plenty of homes available in Reno along the River in Reno. Because I don't know what type of home you're looking for I'll give you a couple examples:
You can find some nice townhomes in downtown Reno along the river at http://www.renoshome.com/downtown-reno.php.
There are also a couple of nice homes in River Run, which is located on the northern tip of Caughlin Ranch. These homes can be seen at http://www.renoshome.com/river-run.php.
If these homes don't spark an interest, you may want to create a custom search along the river at http://www.renoshome.com/river-run.php. Draw a polygon around the areas of interest and select "Refine Search." Homes that are currently available will appear on the map for you to choose from.
I hope this helps,