Ride MATA, Memphis
While the Trolley part of MATA is relatively safe and fun, I would NEVER suggest that a tourist take the city bus anywhere. I made the mistake of doing that while attempting to get to Graceland, and it was absolutely horrible. Lots of beggars, thugs, just a very generally unsafe situation. We were so stressed out by it that we ended off getting off early and walking 1/2 mile (which is also not safe) in order to get away from the other passengers. They were truly scary - we could hear them discussing things like how they commit crimes, etc. PLEASE DO NOT USE THE BUSES, and if you do, go in a big group and/or with big scary men. I have been a lot of places, but that was the most afraid I have personally been.
Downtown Memphis is very walkable, except for having to deal with reckless drivers. However, if you travel farther, or just don't feel like walking, then you can use the Memphis Area Transit Authority (MATA) trams.
Check the website or call the phone number below for prices, schedules, and other information.
If you choose to take the public transportation service in Memphis you'll be using MATA: Memphis Area Transit Authority. I'm not familiar with how MATA works at all, but check out their website if you're interested. You'll probably be okay on the trolley downtown, but I wouldn't really recommend taking the MATA around the city.