Jacksonville is actually a HUGE area - largest city by land area in the "lower 48" states, and the largest city (by population) in Florida. Your best bet is to check the typical travel sites (Travelocity, Expedia, Trip Advisor, etc.) for your dates - check out the rates and read the reviews to find a good match.
If I had to stay somewhere "clean and cheap" this would be it...
http://www.marriott.com/hotels/travel/jaxjs-courtyard-jacksonville-flagler-center/ (I drive past it at least a few times a week.) This is in a nice area on the southside, just off I95 - it's south of the 295 Loop. There is a Chili's, Applebee's, Five Guys, Panera, Starbucks, Japanese steakhouse, pizza, etc. very nearby - not all are within walking distance, though still close.
Anyway, I'm not really sure what your preferences are, as "cheap" and "clean" are both very subjective.

We opt for Marriott due to being rewards members, so there ya go.
