Rock the Wheels for Hub Play

Hold the top of each tire and push it firmly side to side against the frame or fork. Obvious movement means the hub bearings are loose or worn. Some hubs simply need adjusting, but if the bearing surfaces are damaged the honest answer may be a replacement wheel, which changes what the bike is worth to you. Check that the wheel is properly clamped before you judge it, since a loose quick-release lever or thru-axle feels much like bearing play.