As @Whuber stated:

1. use the Euclidean Distance tool on your river data (http://resources.esri.com/help/9.3/ArcGISEngine/java/Gp_ToolRef/spatial_analyst_tools/euclidean_distance.htm).
2. reclassify the output so that distances < 500m = 0, values between 500 and 1500 are 1, and values greater than 1500 are 0. (http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z000000sr000000.htm)

DONE

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)

As @Whuber stated:

1. use the Euclidean Distance tool on your river data (http://resources.esri.com/help/9.3/ArcGISEngine/java/Gp_ToolRef/spatial_analyst_tools/euclidean_distance.htm).
2. reclassify the output so that distances < 500m = 0, values between 500 and 1500 are 1, and values greater than 1500 are 0. (http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z000000sr000000.htm).

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)

As @Whuber stated:

1. use the Euclidean Distance tool on your river data (http://resources.esri.com/help/9.3/ArcGISEngine/java/Gp_ToolRef/spatial_analyst_tools/euclidean_distance.htm).
2. reclassify the output so that distances < 500m = 0, values between 500 and 1500 are 1, and values greater than 1500 are 0. (http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z000000sr000000.htm)

DONE

As @Whuber stated:

1. use the Euclidean Distance tool on your river data (http://resources.esri.com/help/9.3/ArcGISEngine/java/Gp_ToolRef/spatial_analyst_tools/euclidean_distance.htm).
2. reclassify the output so that distances < 500m = 0, values between 500 and 1500 are 1, and values greater than 1500 are 0. (http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009z000000sr000000.htm)

DONE

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)