Once Oppenheimer’s appointment was settled, General Groves explains in Now It Can Be Told: The Story of the Manhattan Project, they had to pick out a location for Project Y:
We needed good transportation, by air and rail, adequate water, a reasonable availability of labor, a temperate climate, to permit year-round construction and out-of-doors experimental work, and all the other things that make for an efficient operation. As before, we sought an isolated area so that near-by communities would not be adversely affected by any unforeseen results from our activities. Yet this installation would be different, because here we were faced with the necessity of importing a group of highly talented specialists, some of whom would be prima donnas, and of keeping them satisfied with their working and living conditions.
[…]
One would lie somewhere along the Santa Fe Railroad, in New Mexico or Arizona, while the other would be in California. The Navy was already interested in the most promising California site, which did not have suitable living conditions from our point of view, and which would have been extremely expensive to develop adequately. While shielded by surrounding mountains against the chance of an accidental explosion, the teeming millions of Los Angeles County were too near for us to maintain the security we deemed necessary.
[…]
I was also certain that it would be extremely difficult and unpleasant to try to keep our scientific personnel from mixing socially with the faculty of the California Institute of Technology. Inevitably, we would have had security breaches, and there would have been just too many people knowing what we were trying to do.
[…]
After Oppenheimer and I had gone over the possibilities at some length, we agreed that there seemed to be nothing that suited our purposes as well as the general vicinity of Albuquerque. There was good rail service between that city and Chicago, Los Angeles, San Francisco and Washington, and all TWA flights to the Coast stopped there. Its climate was excellent, it was well isolated, and had the additional advantage of being far inland, which appealed to me because of the ever-present threat of Japanese interference along the Coast.
Because a New Mexico National Guard regiment had been captured in the Philippines we could count on a population and a state government intensely interested in furthering the war effort. The support we received was superb.
Oppenheimer owned a ranch in the near-by Sangre de Cristo Range, so we could draw upon a firsthand source of information on the general character of the country in judging whether our scientific people might find working there to their liking.
[…]
The only major problem left was whether the school’s owners would object to its being taken over. It was a private school with students from all over the country and, had they chosen to do so, its owners could have made considerable trouble for us, not so much by making us take the condemnation proceedings into court as by causing too many people to talk about what we were doing. When the initial overtures were made to them, I was most relieved to find that they were anxious to get rid of the school, for they had been experiencing great difficulty in obtaining suitable instructors since America had entered the war, and were very happy indeed to sell out to us and close down for the duration — and, as it turned out, forever.