This is a tough one without re-doing the floors. Could you call a tile store? Maybe they have some type of treatment to 'rough up' the tiles. Also, since you have elders in the home, grab bars placed in well thought out locations might be a good idea anyway, along with skid-free rugs.

So many grays turn blue. after much trial and error for bdrm, bath and water closet , i'm happy with Benjamin Moore Horizon and Behr ultra in Burnished Clay. Neither look great on the card but they dry to a soft neutral gray. worth getting samples to try.

I am assuming you haven't finalised your wall colours and colours of any other fixed elements. In case you have finalised your color scheme you would need to see which of these colours blend well or complement with that scheme. Assuming none of this info is available, then you could look at the neutrals which go with all colours. The white tile and the 2 colours at the end would be preferable. If you want color on the floor as well as drama, you can choose from the 2nd options from both sides or even the 1st from left.

antislip and easy maintainance tiles for exterior is the key. choose any shade, colour, size. must not have deep textures as that's gonna be tough later in use. do consider slope and drainage appropriately as terrace may lead to water proofing issues in future. make sure skirting is everywhere and corners with top part of the balcony wall is tiled properly. thanks shradha shah beescheese design