Sharon,
Columbus is a lovely southern city and there are planty of places to stay. I used to work there a few years back, still visit regularly, and have seen the town evolve over the years. Columbus State University's downtown campus and performing arts center, built just a few years ago, an expansive downtown revitalization and corporate investment by Coca Cola, Synovus/TSYS, AFLAC and others have really put a shine on the historic downtown district.
I believe there is lodging directly on Ft. Benning as well - the various service members clubs should have guest houses - but, after OCS, boot camp or jump school, your son's probably okay with some time off-base. I recommend the Marriott downtown or the Gates House (www.gateshouse.com) a wonderful bed and breakfast. Both are right in the historic downtown area and within walking distance to many restaurants and shops. Expect to pay around $120+ per night, though both offer discounts for service members. There are more economical options, though they tend to be further afield from the historical areas. Check out the visitors guide at www.visitcolumbusga.com for more info.
Enjoy your stay in Columbus and thank you for your son's service to our nation!
/Dan