This isn't specific to Spine or Unity. But in Unity, the settings is on the Texture. Select the relevant texture asset in Project view and you should be able to see its inspector.
Try enabling mip mapping and changing the related settings until you get the results you want.
You may end up with something a little too blurry or a little too sharp depending on the resolution of your texture.
The same will be true regardless if you use Spine skeletons, or Sprites, or a 3D model with textures.
