We use a couple of the woven polyester patio mats - got ours online, but I forget where. They work great. They do not absorb water, so they don't get heavy when wet, the water runs right through, and they dry very quickly. They feel good on the feet, and sweep off and fold up easily - ours get stored in the under bed storage area.
While a nice concrete patio pad would be nice, we seldom stay in parks like that - the coastal places we frequent are usually packed sandy soil or crushed stone. We are pretty good at wiping our feet before entering, but the four legged members of our crew are not as careful.
Another nice thing about the woven patio pads is they will not kill the grass like an outdoor carpet. Check out this picture - when we broke camp after a week, the grass was actually greener under the mat than around it. You can see the mats folded up on the picnic table.