The Sherman Hills neighborhood is immediately west of downtown. It is older neighborhood, but I haven't heard of any serious crime activity. Sherman Hills is roughly between MLK Parkway on the west, Heritage Hills/15th Street on the east, I-235 on the north, and Ingersoll on the south. There are some nice duplexes/condos within this area. Friends of mine used to live in this area; I have been there late at night and did not notice any suspicious activity.
Below is a link which details neighborhoods within Des Moines.
Neighborhood Map & List