Found in Oakwood Cemetery, Syracuse, NY:
Capt. Wm. J. Hunt
Died at Chesapeake
Hospital Va.
of wounds rec'd.
before Petersburgh
July 30, 1864.
Ae. 22 y'rs & 4 mo.
I found a scant amount more of information about him from here: Captain William J. Hunt, Co. D, 117th NYSV. Joined July, 1862 at Utica as 1st Lt., age 21; Captain Dec., 1863; WIA June 28, 1864 at Petersburg, VA; died July 31, 1864 at U.S. General Hospital. The death date differs by a day and the hospitals are identified differently.