Mexico City

You'll probably get better responses in the Mexico session.
Mexico City is one of the biggest cities in the world, so it's almost impossible to give you a recommendation on where to stay without knowing what you're after.
Sight-seeing? Business meetings? Visiting family/friends?
It can take 3+ hours to go from one end of the city to the other, so proximity should be high on your priority list.

 

It sounds to me that this is your first time visiting Mexico City. Given how overwhelming that could be, unless you're very adventurous, I'd recommend staying at a hotel.

I'm not very familiar with the East end of the city where the Autodromo is. I don't think there are any decent areas around. So your best bets would be to either:
- By the airport which is fairly close to the Autodromo
- Downtown on Reforma, a bit farther away, but more stuff to do

Alternatively, Polanco or La Condesa would be the other areas I'd look at.