The IUPIU University Library has put the Indianapolis City Directories for 1858-9, 1880, 1914, 1915, 1916, 1917, 1918 and 1920 online.

Note: clicking on ONE image gives you access to HUNDREDS of additional pages after that. The one page is just the "heading."

Also, They aren't in chronological order -- the 1800s ones are at the end, for some reason.

Go to http://indiamond6.ulib.iupui.edu/cdm4/search.php
and type in city directory in the phrase field