We aren't close to ready for Mars. We need a base on the moon.
Mars does have a reasonable atmosphere (albeit not breathable, it's mostly CO2), and therefore does have some hope to be terraformed to earth-like levels. We will probably have to use closed systems (greenhouses with water recycling) until we heat the planet up a bit and get it back to the state it was when it had running water and precipitation.
Asteroids, since I assume they move and possibly in odd orbits might be difficult to reach in emergency situations, I'd rather not see any nation's Astronauts stranded on a remote asteroid.
The problem I would see is finding a big enough NEO asteroid, that you actually can stand on instead of floating by its side, or having to worry about reaching escape velocity if you jump strongly enough.
If one's willing to go to any asteroid, not just NEO, then Ceres could be a possibility. A quick search says the delta-v required to reach it from LEO is about half that to reach Mars' surface.
I suppose it would be helpful to build some kind of centrifuge in any base to simulate gravity, as well.