If you're looking to get to know Little Rock and don't mind a little exercise, why not try walking? Downtown parking and traffic can be hectic so my preferred way to see the sights is by foot. I've included the exact address of most of the attractions so you can print out a map with one of the popular mapping softwares available on the web.
Start your walk at Riverfront Park. Riverfront Park is the perfect place to take a relaxing morning walk. There is a promenade with interesting facts about the settlement of Little Rock and toward the north end of Rock Street you can see "Let Petite Roche," the rock that Little Rock was named after. Riverfront Park can be found behind the Peabody Hotel on Scott Street (Riverfront Park, N Scott St, Little Rock, AR 72201). This area has plenty of parking, but you generally have to pay to park.
Not too far from the Peabody is the Old State House. The Old State House is Arkansas original state capitol. The building is kept in Victorian style and houses some great Arkansas history. (300 W Markham St, Little Rock, AR 72201).
Take some time to browse the shops and restaurants that line the Rivermarket district. Just be sure to mark your faves so you can come back when the market clubs and bars really get jumping at night. The Rivermarket is on President Clinton Avenue.
Just a few paces away from The Rivermarket and Riverfront Park is the Historic Arkansas Museum. The Historic Arkansas Museum features five pre-Civil War houses that have been restored to antebellum appearances. Guided tours of the historic houses are available for a fee, but self-guided tours are free. Cross President Clinton Avenue at LaHarpe Boulevard to enter the museum. Historic Arkansas Museum, 200 E 3rd St, Little Rock, AR 72201.
For the brave and healthy, you can hike down to the Capitol Building. The building was built over a century ago as a replica of the U.S. Capitol Building, and has been used in many movies as a stand in. The building is open to the public Monday through Friday from 7 am to 5 pm. However, the trek from the Historic Arkansas Museum may be a bit much for some. You might want to add this one to your driving tour! It is located at the intersection between Woodlane & Capitol Avenue.