The biggest problem with bench advertising is that many cities and towns will want to put it out to public bid. Normally, bench advertising is on the public right-ot-way, although you can still pull it off if you stick it back off the sidewalk and into the private property line.
Yes, get the ordinances and see what's allowed. If it looks like it has a shot, give it a try. I am into testing any idea in the real world to see if it works out. If you don't like it, or the opportunity is not as big as you thought, you can always shut it down or sell it.
As Sam Walton used to always say when somebody ran a new idea by him: "do it, try it, fix it."