There are several very good restaurants in Conway. It is going to depend on the type of food you are looking for.
Top of the choice for me on date night is the Rivertown Bistro- www.rivertownbistro.net, in the historical downtown. This restaurant has the fine dinning feel and food with the laid back southern charm, shorts/golf shirt/flip flops. Recommend the “Low Country Spring Rolls or Lobster and Lump Crab Cake” and “Parmesan Roasted Chicken”.
My favorite for the family night is the Riverwalk Grille. For a local favorite that has different varied menu you can get burger/wrap/daily special. The daily special can compete with the best on most nights. Here the weekday lunch and Friday night crowd is pretty busy. Other than that, it is a good bet.