A great way to find this data is to go to FunnelScope.com, and search for the city you want with "budget" attribute checked off. Here's the result: http://www.funnelscope.com/Florida-FL/Ja...
Note - there's some really shady hotels in downtown Jacksonville. Avoid. A few are crack dens. Not joking.
You won't get a hotel in Jax that's anything but a flee pit for $50 a night. However there is stacks of choice for cheap hotels/motels. It's difficult to recommend a place because it's a huge city in terms of area and it depends where you want or need to be. Most of the cheaper hotels are at the exits of I-95 I-10 and I-295.
3. Dean C
As stated earlier it would help if we knew what part of Jacksonville you want to be in. What are you coming here for? How are you getting here? A little more info and we can probably find you something
Try the extended-stay places: InTown Suites, Suburban Suites, etc. For example, the Suburban on Phillips (near Baymeadows) is something like $50 nightly or 30-something if on the weekly rate.