Rent a car...public transit sucks here, and cabs are very expensive.
Overton Square and Cooper-Young are where Memphians go...Beale is fun, but it's mostly tourists.
Boscos and Local are great at Overton Square (get the made in house Flaming Stone beer from Boscos)
Sweet Grass, Young Ave Deli (it's also a nightclub), and Soul Fish Cafe are great...they're at Cooper-Young
Central BBQ and the BBQ Shop are very good.
Go get a drink at the Peaybody and checkout the rooftop
The main attraction will be the Memphis Zoo...it's really the cities gem.
Graceland is cool...but it's a bad part of town...just a heads up.
Sun Studios is a fun tour...takes maybe an hour or so.