Pinnacle Mountain is a great hike! It is steep, though, so be prepared with some water and good shoes. The West Summit Trailhead is much easier than the East Trailhead.
They have tasting tours which are a lot of fun! I'd recommend making reservations ahead of time. If you don't want to take a tour, they have a bar and shop inside the Distillery.
One of our favorite coffee places in Little Rock!
The river market is a great place to walk around and find restaurants - my favorite is the coffee shop, Mugs, on the North Little Rock side. It is free to ride the trolley around.
This is a nice paved walk over the Big Dam Bridge.
We recommend the Cedar Falls Trail.
Hot Springs makes for a great day trip if you have time. We recommend visiting the Bathhouse Row, Garvan Gardens, and grabbing lunch at McClards BBQ (the Tamale Spread is the best).