If you have any Hilton Hhonors points, there are a couple of their brands between the airport and downtown that are less clostly than downtown hotels, but you will need a car. There's a Hampton Inn and a Homewood Suites on Governor's Row. From there it's only about 6 or 7 minutes to the Congress Avenue offramp. Plenty of places to eat on So. Congress. Magnolia Cafe is fun...food is just ordinary, but the coffee is good and they serve breakfast all day.
Then, when you have time, drive on over to Whole Foods at 525 N. Lamar. It's a destination in itself. You can park under the store in the lot.