How can I select a recreation site location based on the criterion that it should AT LEAST be 500 m from a river (shapefile) and AT MOST 15000 m from the same river using Spatial Analyst Extension?
As @Whuber stated:
Note: this could be tedious depending on what your cell size is. so as an alternative you may want to convert the raster to a shapefile, add a field "suitable" and then use field calculator.
If you have other criteria, do the same thing on each. Then use the raster calculator, add up the values, those with the highest scores are most suitable (assuming all variables are equally weighted in your analysis)
If you're using a shapefile why not create a multi ring buffer, 0-499m and 500-15000m. Then anything that falls in the outer ring meets your criteria.