Individual Details

James never married.

1870 Census. Talkington, Sangamon, Illinois. Living in the household of Thomas and Jane A. R. Mitchel and family: James W. Alexander, age 26, School Teacher, b. Ohio.

1880 Census. Auburn, Sangamon, Illinois. Living in the householdof George and Mary Sinniger and family: James Alexander, boarder, age 36, Teacher, b. Ohio

1890 Veterans Schedules
Martins Ferry, Belmont Co, Ohio
#38 James W. Alexander, Private, Co G, 170th Ohio Infantry. Enlisted 10 Mar 1864; discharged 10 sep 1864.

1900 Census. James was back in Martins Ferry, Belmont Co, Ohio, Pease Twp.
Hh 271, living by himself.
James Alexander, b. Apr 1844, age 56, Single, b. Ohio, Farm Laborer, renting.

1910 Census. Ohio Soldiers & Sailors Home, Perkins Twp, Erie Co, Ohio
James Alexander, age 66, single, b. Ohio

http://www.ohiohistorycentral.org/entry.php?rec=2172
Ohio Soldiers' and Sailors' Home
In 1886, the Ohio General Assembly authorized the creation of the Ohio Soldiers' and Sailors' Home at Sandusky, Ohio. The home was created to provide for Ohio's indigent honorably discharged veterans of the American Civil War. The institution's first board of trustees selected a site just south of Sandusky, Ohio. The city government agreed to provide streetcar service and gas, water, and electric power to the site.
On November 19, 1888, the first seventeen Civil War veterans arrived at the Ohio Soldiers' and Sailors' Home. Originally, the home provided housing and food for the veterans. Beginning in 1950, the institution also provided nursing home care. As the United States became involved in other conflicts, the Ohio Soldiers' and Sailors' Home admitted honorably discharged veterans from these wars as well. Veterans from the following conflicts in the twentieth century have resided in the home: the Mexican Border War, World War I, World War II, the Korean War, the Vietnam War, and the Persian Gulf War. The home also has been opened to veterans of all military branches, including the U.S. Army, the U.S. Navy, the U.S. Air Force, the U.S. Marines, the U.S. Coast Guard, and the National Guard. After 1969, women veterans could also seek assistance at the institution.
By 2005, more than fifty thousand veterans had resided at what was now known as the Ohio Veterans Home. In that same year, approximately 660 veterans lived at the Ohio Veterans Home, including 427 people in the nursing home component. In 2003, a second Ohio Veterans Home was opened in Georgetown, Ohio. If a veteran is destitute, he or she now receives free care at the Ohio Veterans Home. Otherwise, the home charges a fee based on a person's wealth. Both the Sandusky and Georgetown sites are operated by the Ohio Veterans Home Agency.

Here is a James W. Alexander from Ohio, also born 1844, listed as being in a home in Illinois. He had lost an eye. Served 1st in the W. VA, Light Artillary from Wheeling, and then in the 170th Ohio Infantry.
U.S. National Homes for Disabled Volunteer Soldiers, 1866-1938
Name: James W Alexander
Birth Year: abt 1844
Birth State: Ohio
Admitted Year: 1901
Age at Admission: 57
State: Illinois
County: Vermillion
City: Danville

This would seem to be the same as the above James W. Alexander. Listed as enlisting 2 May 1864 in Bellaire, Ohio; discharged 10 Sep 1864 at Columbus, Ohio. However the information doesn't quite match.
Name: James W Alexander
Age at enlistment: 20
Enlistment Date: 5 Feb 1864
Rank at enlistment: Private
State Served: Ohio
Was Wounded?: Yes
Survived the War?: Yes
Service Record: Enlisted in Company G, Ohio 170th Infantry Regiment on 14 May 1864.
Birth Date: abt 1844
Sources: Official Roster of the Soldiers of the State of Ohio

The 170th was part of the National Guard.

Another James W. Alexander served in the 49th Regt, Illinois Infantry, Co D, as a private. He is listed with an alternate name of James M. Alexander.

Ohio Deaths, 1908-1953, FamilySearch.org
James W. Alexander died 25 Jan 1914, Perkins Twp, Erie Co, OH. He was 69, single, born April 1844. His father was Peter Alexander; his mother Catherine Mitchell, both born in Ohio.

Birth	1844	Belmont County, Ohio
Death	25 Jan 1914	Erie County, Ohio

Father	Peter Alexander (1804 - 1862)
Mother	Catherine Mitchell (1809 - 1885)
Sibling	Albert James Alexander (1832 - 1839)
Sibling	Elphenor Americas Alexander (1834 - )
Sibling	Ross Wilson Alexander (1835 - 1839)
Sibling	Josephine Catherine Alexander (1837 - 1852)
Sibling	Elvira Isabella Alexander (1839 - 1920)
Sibling	Lorinda Adelade Alexander (1840 - 1911)
Sibling	Martha Melissa Alexander (1847 - 1919)
Sibling	Mary Sanders Alexander (1849 - )