I have never seen the picture. But with a quick google search of the visible caption I was able to come up with the following:
The ship is the USS Boise CL-47. A cruiser. The photo was taken sometime during the month of November 1942. The part of the caption I can see indicates that the ship had six(based on the number of fingers held up) "kills" in battle. The ship was arriving in the Philadelphia Navy Yard, Pennsylvania, for battle damage repairs, November 1942. She had been hit by enemy shellfire in the Battle of Cape Esperance on 12 October 1942, resulting in a large fire that burned out her three forward 6"/47 gun turrets and their ammunition spaces. This according to the following link:
http://www.navsource.org/archives/04/04047.htmYou could check the archives of the Philadelphia newspapers for that time. The paper or the local library in Philly should have them on microfilm.
Here's a link to a memories website with details about the ship and crew:
http://www.wartimememories.co.uk/ships/boise.htmlIf your grandad is the Marine in the picture then he would have been part of the Marine contingent at Guadalcanal Sept 1942 according the second website I linked.
I know this isn't much, but maybe it can point you in the right direction.