The secret military base in the desert in Grand Theft Auto: San Andreas is called Area 69. It is a heavily restricted government research facility located in Bone County, in the desert region near Las Venturas.
Area 69 is Rockstar's parody of the real-world Area 51 in southern Nevada. The name adds the series' characteristic adult joke, while the location's secrecy, military security, underground facilities, and rumors of experimental technology echo popular Area 51 conspiracy theories.
The base becomes especially important during the mission "Black Project." Carl "CJ" Johnson infiltrates the facility to steal a government-developed jetpack for The Truth. The mission involves avoiding or fighting military personnel and escaping with the stolen equipment.
Verdant Meadows is a desert airstrip that CJ acquires and develops, not the secret base itself. Bone County is the surrounding region, and Fort Carson is a nearby desert town. Those choices are geographically related, which makes them plausible distractors, but Area 69 is the single canonical answer.