Looked at these topo quads today at the library:  Aqua Fria, Tetilla Peak and Santo Domingo.  Looked at a lot more but these were the relevant ones to follow the course of the Santa Fe River to the Rio Grande.

Here are my notes:  Cienega Creek is a tributary of the Santa Fe River.  Santa Fe River comes toward La Cienega from the northeast and travels between Cerro Seguro and the Las Tetillitas peaks.  Santa Fe River then runs through the Cañada de Santa Fe which skirts southern edge of Tsinat and La Bajada mesas.  Tsinat Mesa has Tsinat Ruins on it.  La Bajada Mesa seems to be the southern edge of the Caja del Rio Plateau and Tsinat Mesa is a small part of La Bajada Mesa.   On its way to the Rio Grande, it appears that the Santa Fe River crosses (over or under?) a spillway of Cochiti Dam but Cochiti Lake is well north of the Santa Fe River.  The Santa Fe River, which originates in the Sangre de Cristo Mountains, goes into the Rio Grande (usually as a dry riverbed) catty-corner across from where Peralta Canyon, which originates in the Jemez Mountains, intersects the Rio Grande.

It seems the Santa Fe River would get an infusion of water from spring-fed Cienega Creek but it it's complicated.  I found online a Channel 4 KOB-TV news report about the village of La Bajada, west of La Cienega and Santa Fe.  The villagers, many who subsistence farm their land, complained last July about no water in the Santa Fe River.   According to the TV station's story, when Santa Fe tore out invasive salt cedar and Russian olive trees further upstream along the Santa Fe River and replaced them with native willows and cottonwoods, beavers toppled those trees and built dams which dried out downstream La Bajada!