Speaking as a guy who adjuncts at a big university, I have to second the guy who works in ed tech. In addition to the comments above, you also stand a better chance of getting more qualified instructors at a community college. I taught lower-division math classes as a graduate student. Indeed, much of the teaching load in many departments is handed over to TAs at big universities. Community colleges often teach exactly the same classes out of the same books, but the instructors will hopefully have (a) better credentials (a masters in their field, though there are a disturbing number of people at community colleges who have masters in ed) and (b) more experience teaching.
Another point in favor of community colleges is class size. At a big university, classes can be huge. A calculus class that I TAed for had over two hundred students in a lecture hall. Yes, they broke apart into smaller recitation sections once a week, but recitation time with a TA is not the same as face time with a professor. Community college classes tend to be much smaller.
Unless you are trying to finish your degree in a top-tier, private institution (Stanford, University of Chicago, Harvard, &c) or a small, residential liberal arts college, there is no reason not to finish an associates degree at a local community college then transfer to a local university (or apply to an out-of-state institution, where you probably have a pretty good chance of being accepted).