There were four main sites during the Manhattan Project. Specifically, two research facilities in Chicago and Los Alamos (New Mexico), and two complexes in Tennessee and Washington State for the actual creation of the atomic bomb.
The initial theoretical work was done in Chicago, because there was a large concentration of nuclear scientists and some existing facilities. In 1942 and into 1943, experimental work was done on controlling the fission process in nuclear reactors, using first graphite, and later heavy water.
By 1943, continuing the experiments in Chicago was deemed too dangerous, and the theoretical and experimental work on the bomb mechanism was moved to newly built facilities in Los Alamos, New Mexico, which was far from cities, and was therefore isolated from the general population.
The actual "manufacturing" (e.g. of plutonium from uranium), was initially done at a newly built complex at Oak Ridge Tennessee, which had the advantages of cheap hydroelectric power produced by the government-supported Tennessee Valley Authority, and was "somewhat" remote from population centers. Later, it was decided that nearby Knoxville constituted a population center, so a new, even more remote manufacturing facility was built at Richland, Washington (the Hanford facility), which had hydrolectric power from the Snake River, but was farther away from cities than Oak Ridge.
There were also a large number of "satellite" facilities, each with specialized functions, but this covers the main ones.