Answer by taking a quote from the following article:

Paul Warfield Tibbets Jr. was born in Quincy, Illinois, on 23 February 1915, the son of Paul Warfield Tibbets Sr. and his wife, Enola Gay Tibbets. When he was five years old the family moved to Davenport, Iowa, and then to Iowa's capital, Des Moines, where he was raised, and where his father became a confections wholesaler. When he was eight, his family moved to Hialeah, Florida, to escape from harsh midwestern winters. As a boy he was very interested in flying.

The 509th Composite Group returned to the United States on 6 November 1945, and was stationed at Roswell Army Airfield, New Mexico. Colonel William H. Blanchard replaced Tibbets as group commander on 22 January 1946, and also became the first commander of the 509th Bombardment Wing, the successor to the 509th Composite Group. Tibbets was a technical advisor to the 1946 Operation Crossroads nuclear tests at Bikini Atoll in the Pacific, but he and his Enola Gay crew were not chosen to drop another atomic bomb.  Tibbets then attended the Air Command and Staff School at Maxwell Air Force Base, Alabama. On graduating in 1947 he was posted to the Directorate of Requirements at Air Force Headquarters at the Pentagon. When the head of the directorate, Brigadier General Thomas S. Power, was posted to London as air attache, he was replaced by Brigadier General Carl Brandt. Brandt appointed Tibbets as director of Directorate of Requirements's Strategic Air Division, which was responsible for drawing up requirements for future bombers. Tibbets was convinced that the bombers of the future would be jet aircraft and thus became involved in the Boeing B-47 Stratojet program. He subsequently served as B-47 project officer at Boeing in Wichita from July 1950 until February 1952. He then became commander of the Proof Test Division at Eglin Air Force Base in Valparaiso, Florida, where flight testing of the B-47 was conducted.  Tibbets returned to Maxwell Air Force Base, where he attended the Air War College. After he graduated in June 1955, he became Director of War Plans at the Allied Air Forces in Central Europe Headquarters at Fontainebleau, France. He left Lucy and his sons behind in Alabama, and he and Lucy divorced that year. During his posting to France, he met a French divorcee named Andrea Quattrehomme, who became his second wife. He returned to the United States in February 1956 to command the 308th Bombardment Wing at Hunter Air Force Base, Georgia, and married her in the base chapel on 4 May 1956. They had a son, James Tibbets.  In January 1958, Tibbets became commander of the 6th Air Division at MacDill Air Force Base, Florida. and was promoted to brigadier general in 1959. This was followed by another tour of duty at the Pentagon as director of Management Analysis. In July 1962, he was assigned to the Joint Chiefs of Staff as deputy director for operations, and then, in June 1963, as deputy director for the National Military Command System. In 1964, Tibbets was named military attache in India. He spent 22 months there on this posting, which ended in June 1966. He retired from the United States Air Force (USAF) on 31 August 1966.

Did he work at any other bases ?
he became Director of War Plans at the Allied Air Forces in Central Europe Headquarters at Fontainebleau, France.