I'm with Kendrah on the waterhog mats. I have one at every entrance to my house. Even if you tile you need something like that, so maybe you could have a wood foyer. Where I live now my first floor is all wood. They make waterhog mats in a lot of different sizes so get one as large as you think you will need. Granted they're not as pretty as an area rug, but I love the practicality. We get some snow and plenty of rain where I live. Also look at ruggables washable rugs which are also popular with people on this site. My next door neighbor just bought a couple of them.
For the best advice, post a picture of the area you're referring to so everyone can see what you're dealing with.
Q