We just bought a house that has a side patio. Its one of those attached to the house off the living room with columns around it but no walls (only a roof).

Currently it has asterturf covering the cement floor. We would like to change that but are wondering what is best - tile, wood, area rug...

Thanks

It's going to depend on the height to your threshold (bottom of the doorway) which I suspect is only 1"..

The best finish then would be a nice epoxy, a very durable paint type of product.

If you have the room you can place sleepers & attach a decking... in that case a composite such as Trex, due to the proximity of the concrete & splashback.
http://www.trex.com/
You, theoretically, can screw the trex right to the concrete but you'd need to get the stock parallel to the slope which would be perpendicular to the house.. may look funky.

You also could look into a concrete refinsh & stamp process (let me see if I can find that url) here it is.. http://www.quikrete.com/diy/SpecialConcreteFinishes.html

http://www.altereagle.com/
http://decks-ca.com
http://kingofcrown.com

Alter Eagle Construction & Design