We have this mat:
http://a.co/3YyixCg
We use this at the bottom of our stairs because our 3 year old will sometimes just randomly wipe out on the staircase just sitting on a step. Crazy kid. However, since we got it, she lands on it (sometimes head first) and just gets right up and keeps on going. It's thick and cushy, and every adult who has stepped on it has commented on how great it feels. It's really great! The edges are beveled and I can't see it harming any floors, and it's not a perfectly smooth/shiny finish. There's a little bit of grippy texture so you don't slip. It's way better than the one we have in the kitchen.