We present interferometric measurements obtained with the CHARA Array of 13 adolescent-age stars in nearby moving groups. The motivation was to spatially resolve the largest stars and to search for binary companions. Nine stars have diameters smaller than the resolution limit and no evidence for companions within 0.5-50mas and {Delta}H<2.0mag. The diameters of three stars were spatially resolved: GJ 159 (0.582+/-0.016mas) and GJ 393 (0.564+/-0.021mas) in the AB Dor moving group, and former member HD 89744 (0.556+/-0.032mas). Combining the angular diameters with their distances and bolometric fluxes, we measured radii and effective temperatures. The temperatures of GJ 159 (6286+/-123K) and GJ 393 (3515+/-68K) are consistent with spectroscopic measurements. Comparisons with evolutionary models show that HD 89744 has evolved off the main sequence. GJ 159 and GJ 393 lie within 1.5{sigma} of the zero-age main sequence, complicating their age estimates because it is unclear whether the stars are contracting or expanding. GJ 159 has a mass of 1.2+/-0.1M_{sun}_ with an age spanning 0.021-3.0Gyr. Its debris disk and lithium abundance favor a young age. GJ 393 has a mass of 0.42+/-0.03M_{sun}_ and a lower limit on its age 0.06Gyr. This overlaps with the age of the moving group; however, an older age would be more consistent with its slow rotation, low activity, and luminosity, suggesting that GJ 393 is a kinematic interloper.