Your first answer gave you a lot of good answers...but I will disagree on one point, usually weekend rates for downtown hotels are a lot cheaper than during the week...Atlanta is more of a business town and not so much for tourists.
My favorite is the Embassy Suites...great rooms, good rates and a first rate hot breakfast, as good as any restaurant buffet. It's right across the street from the Omni Hotel; a very short walk to the Dome and/or Phillips Arena; and has a Ruth Chris Steak House right next door. Check out the Tabernacle (it's also a short walk away) and see if they're having a concert the same weekend and maybe have two good times (and there's a Ted's Montana Grill across the street from it).
There are a lot of nice hotels very close to the Dome.
The Omni @ CNN Center, Embassy Suites, Hilton, Westin, Days Inn to name just a few.
The Dome is right in the heart of downtown Atlanta so there are many choices. Most will be expensive.
Read the reviews. If you are going to stay near Georgia Dome, these hotels are nice one's and have good reviews.
Omni Hotel Cnn Center Atlanta http://hotels.americacheaphotels.com/Hot...
Glenn Hotel Atlanta http://hotels.americacheaphotels.com/Hot...
Hilton Garden Inn Downtown Atlanta http://hotels.americacheaphotels.com/Hot...
Holiday Inn Downtown Centennial Park... http://hotels.americacheaphotels.com/Hotel/Holiday_Inn_Downtown_Centennial_Park_Atlanta_Georgia.htm
Marriott Hotel Downtown Atlanta http://hotels.americacheaphotels.com/Hotel/Marriott_Hotel_Downtown_Atlanta_Georgia.htm
Atlanta (Georgia) hotels http://hotels.americacheaphotels.com/City/Atlanta_Georgia.htm
Call any local cab company and tell the Dispatcher you were told to call because someone said he/or/she knew Atlanta like the back of their hand... etc etc. and do they have time to help you with a personal question?
Safe, haha. Nowhere.