I always used to stay at the Marriott, but the last few years they've enacted something called "Passkey," which is a system you have to use to book rooms for DragonCon now. Basically it was the case that if you didn't get on Passkey and book a room the second they went on sale, you probably wouldn't get one. However, several things have changed for next year which can affect this. One is that now Marriott rooms have a non-refundable one night deposit. The rooms are also apparently non-transferrable. So this might make it easier to book a room at the Marriott, since less people will be reserving multiple rooms. However, you run the risk (if you can't go) of losing somewhere around $200 bucks. And since you have to reserve so far in advance, who knows what can happen in a year? I'll also add that the Marriott used to be pretty quiet, but now it's very busy with an active bar on the top lobby floor, and the white noise from all the people can be heard up in the rooms, even if you're up pretty high. This didn't bother me much, but it's another consideration. Also, it can be really hard to get elevators there, especially on checkout day. I'm not sure when Passkey reservations open up for DragonCon 2013.
I don't have experience with staying at the Hyatt.
The Hilton also has a one night non-refundable deposit. And I've heard it's already booked up. (Though, it might still be worth calling to make sure this is true.) After last year, when I couldn't attend DragonCon 2011 because of a serious, last-minute health issue, I ran into problems with the Hilton reservation I'd made. So never again will I take a chance on a non-refundable deposit room.
The Sheraton will charge you a one-night deposit, but it is refundable up until a few days before the Con. (Or maybe even less, not sure exactly.) The rooms are quiet, and you can catch elevators without a problem. I used to think it was off the beaten path, but DragonCon has spread out so much, that it's not really. You'll have to pick up your registration at the Sheraton and BritTrack and TrekTrack both have panels here. The Sunday night Yule Ball (sponsored by the YA Lit track) is here as well.
The only disadvantage is that you have to walk outside to get to it, there aren't tunnels like there are for the other hotels. (You might have to go outside to get to the Westin too, but I didn't end up going there at all this last Con.) However, the tunnels are so crowded (especially Saturday) that I found it was a relief to be able to walk outside. So that's not a big deal unless there is rain, or you are in a delicate costume. But you may have lots of indoor walking to do regardless of that. Tunnels connect the Marriott, Peachtree Center Mall and Hyatt, and now the Hilton, but it can still be a lot of walking.
So based on all that, I booked a room at the Sheraton again for this year. I didn't have a problem going to friends room parties or hanging out with them at the Marriott. There are lots of people walking back and forth at all hours, so I never felt unsafe walking between hotels, even at night. (At least, no more unsafe than you'd feel at DragonCon in general.) And my fears about being really far away were pretty unfounded. The Sheraton is already taking reservations.