I can put forth a few places:
Arkansas--Helena, Fayetteville, Fort Smith (after it's recapture in 1863).
Missouri--Benton Barracks, volunteers training and US and USCT Regulars, Pre war, early in war, and post war at Jefferson Barracks,
(During the war it was mostly a hospital site), and at Springfield.
Massachusetts--Boston-- Camp Meigs: 54th and 55th Mass. Inf. Regts. were organized and trained there.
Illinois--Chicago recruitment center of the 29th USCT, maybe at Camp Douglas, Ill. organized at Quincy, Ill.
Pennsylvania--Carlisle Barracks, home of the mounted recruiting service. It recruited and trained enlisted men and officers for the cavalry.
The Mounted Recruiting Service had centers in 19 cities across the US. They were: Boston, Mass. (1861-63), Cincinnatti, Oh. (1861-65), New York City, Ny. (1861-65), Wheeling, Va. (62-63), Buffalo, Ny. (1862-63), Norristown, Pa. (1862), Cleveland, Oh. (1862-65), Indianapolis, Ind. (1862-63), Baltimore, Md. (62 and 65), Pittsburg, Pa. (1862-65), Philadelphia, Pa. (1862-65), Chicago, Ill. (1862), Detroit, Mi. (1862-63), Elmira, Ny. (1862-63), Washington, D.C. (1862-63), Harrisburg, Pa. (1863-65), Madison, Wis. (1864), Rochester, Ny. (1864-65), and St. Louis, Mo. (1864). Some of these were only open for months. There were also other recruitment centers opened locally by the Cavalry Regiments 1st--6th,where ever they might be stationed.
The US Regular Artillery was also recruited by the MRS at Carlisle.
US Regular Infantry Recruitment was carried out from October to December 1862 at Washington D.C., Harper's Ferry near Md., and near Nashville, Tenn. There is also information that says US Regular Infantry Regiments were recruited in small towns, such as the 16th near Rouse's Point, NY. It was mustered in at Albany, NY. It was originally called the 1st NY Northern Infantry. Evidently the recruitment of US Regular Infantry was a problem. One sees recruiting of various regiments during the war in different cities, like the 15th US Infantry Regiment at Philadelphia. There were usually bounties of $100., offered for joining up during the war.