But after Geneseo she went to Monmouth, Illinois to attend the college there. That's about 800 miles away. Monmouth was Presbyterian and an early co-ed college. But there were closer alternatives: Elmira College which her daughter Helen would attend, and Cornell, which two grandchildren would attend. Elmira, at least, was both associated with the Presbyterian church and only for women. But it seems to have had some controversies in the 1870's which might have told against it. My guess is that one or more graduates of Monmouth College were involved in the founding or running of Geneseo, and recommended Ada to the college and the college to Ada.
One excerpt from the Monmouth College history:
"Greek Life firsts
In the college’s early years, college women enjoyed equal footing with their male counterparts — unusual for that time. This sense of equality helped inspire the birth of the sorority movement at Monmouth. When veterans returning to the college from the Civil War decided to form fraternities, a group of women was determined not to be outdone. In 1867 they established the first fraternity for women, known today as Pi Beta Phi. Three years later, another famous women’s fraternity, Kappa Kappa Gamma, was founded at Monmouth.