USS Razorback - WW2 era sub you can tour.
Central High School National Site. They have interactive videos in the park building. Go to the end of the building closest to the street/school. As you watch the videos, you can look outside and see where history took place.
Old State House Museum
Historic Arkansas Museum
MacArthur Museum
The Riverfront area is nice. If you are in that area, you can take the trolley or drive to North Little Rock and the Argenta district. Stop by the Argenta Market for a bite to eat. The Old Mill is also in N.L.R featured in Gone with the Wind
I didn't care for the Clinton Library, if you do go, don't eat in the downstairs cafe, too expensive.
If you want something different to eat, check out Cafe Bossa Nova. I liked it