What is the largest United States city without public transit? My guess is Yuma, AZ. The population is about 75,000 and they have no bus or rail service outside of Greyhound.
Yuma is a stop on Amtrak’s Sunset Limited (Los Angeles CA to Orlando FL) train, so there is rail service.
As regards local transit, Yuma County Area Transit (YCAT) runs a couple of scheduled routes in and around the city of Yuma.
So, whatever the factual answer to your question turns out to be, it’s not going to be Yuma.
According to several sources on the Web, it’s Arlington, Texas (2000 Census pop 332,969). There’s a publication (dated July 19, 2003, and it’s a PDF file) by a professor at the School of Urban and Public Affairs at the University of Texas at Arlington that confirms this.
So, unless someone can show that either (a) Arlington TX has put in a transit service since July 2003 or (b) there’s a more populous US city without public transit, I’d say Arlington’s your answer.
Arlington TX does appear to have transit service for the disabled, but it could easily be claimed that such services are not true “public transit”.