You can look up WWII Army Enlistments at the online NARA website:http://aad.archives.gov/aad/
click on WWII. It will give you the place enlisted and his "native" home or county and state he lived in at the time of his enlistment. As well as his all important Military Service Number.
Also click on "Military Personnel" and do a search of his name.
Now if he was a Marine, they are connected to the Navy and I know Ancestry has some Marine and Naval Enlistment databases.
Is he buried in a Veteran's Cemetery? Look here:http://gravelocator.cem.va.gov/
If he never married then next of kin can be nephews but there maybe a fee involved in getting a copy of his service record. You need to be a more direct next of kin to get a free copy. Unless they have changed the regulation since i got my father's and grandfather's records.
Other website you may glean information from:
click on state enlisted from or lived in. Then the county once you get to the state.
see if any other records available that can help.
If you know the state and city he moved to after his discharge check the local county court house to see if he filed a copy of his DD214 (discharge papers) with the county recorders or family court office. All Veterans were encouraged to do so, so if they lost their copies they could access the copy there to get future G.I. Benefits, state and Federal, as they were enacted.
Ancestry and Fold3 have Military databases, either subscribe yourself or see if your local library or LDS Family History Center has them to use.