I have a cute old apartment and I want to update the kitchen
There is a special paint you can use on tiles...check with Home Depot or Lowes or you can stencil a flower or whatever you like on some of the tiles to update
Rustoleum or Homax tub and tile kits are epoxy based.
Painting is an option
peel and stick backsplash
Try cleaning the grout first with baking soda and water and a dish scrubber (not a scratchy abrasive). If that works, you won't need to re-grout. I have cleaned several sixty year old ALL TILE bathrooms that were totally rejuvenated.