Mars is closer than the asteroid belt for one. We know more about Mars, its resources, its seasons, its orbit. A stepping stone to building a colony on Mars.
We know that lack of gravity has adverse effects on the human body.
Land astronauts on a asteroid sounds like another 0bama - Dr James Henson pie in the sky failure in the making without a long term plan.
Unfortunately, soft landing on Mars is impossible with rockets that we have (or know about.) Mars is worse than the Moon. The reason is that it has atmosphere. The atmosphere is too thin for a winged lander (Shuttle) or a parachute, but too dense for a vertical rocket-assisted landing.
The latter is not obvious, but it had been discussed many times on science and astronautics blogs. The rocket engine is open at the nozzle end. The incoming atmosphere, at many a Mach number, will create resonances within the chamber of the engine. Those resonances can completely shut the engine down, or interfere with it enough for you to drop like a stone (doesn't take much - failure of your only braking engine at 10 miles above Mars is not recoverable.)
Ideally, you land on Mars on gravity engines. Unfortunately, the blueprints of those are locked in a safe at Area 51 :-)
Landing on asteroids is not a landing at all, it's more like matching speeds and then drifting close enough to fire a harpoon and pull the ship closer. To start in the opposite direction you simply cut the rope and do whatever you want - the asteroid is not going to interfere and you don't need to use fuel to escape its gravity (it's negligible.) On the other hand, asteroids are pretty far away, and you may need some considerable fuel reserves to just keep the ship running for a couple of years that it takes to get there and back.
All in all, I don't see a good reason to send humans anywhere beyond the Moon. Planets, starting with Mars, are just too far away and humans are too short-lived and human engines are too weak. If you want, make a rocket with nuclear engines, and send robots to other planets. They will get there faster, and they don't need to return. Even today we have pretty decent mechanisms. They aren't proper thinking robots yet, but that is not even required, as long as the probe reports its findings every day and listens for instructions. There is no hurry, the probe can sit there, charge batteries or whatever it is doing in idle time, and wait until the controllers tell it what needs to be done.
There is an even better reason to send probes instead of humans. We need to test many asteroids, not just one. We need to know statistics about their composition. Testing of one piece of stone is pointless. Machines will do the testing better than humans; humans, after all, only can insert the sample into the machine - they can't use their eyes or other senses to test for chemicals. So why to send a valuable biological sample handling device (a human) when you can send an automated drill?
Ultimately, access to the space depends on good, clean, affordable engines. What we have now is neither. Every launch costs a small kingdom, and the mass that is delivered into orbit is fairly small. We have no engines to efficiently go beyond the LEO. It would be most important to develop those; nuclear propulsion is one possibility, but there are other. Most importantly, those engines should use reactive mass that can be found outside of Earth; water is one such option. We wouldn't want to buy a car that is pre-fueled at the factory and can't be refueled by the owner; so why do we accept that in rockets?