The 90’s tile with every tile with the same ‘stone’ print does hurt the eyes. As to painting versus leaving stained it’s hard to say without seeing the whole space. Design is contextual.

Here is a picture

*better picture . We are in the process of painting the walls as well.

I would leave the wood, since it matches the rounded windows and your furnishings so nicely, however, I would definitely redo the tile, to something that suits your taste and goes with your furnishings. The pattern on the tile now, is a very boring repeat pattern.

What if I paint the windows white in the future for a more modern look?

In that case, I would paint the fireplace surround too. However, I really like the rounded windows and the fireplace just the way it is.

I hate the skinny trim and having it dark emphasizes how narrow it is especially since the windows aren’t wood. I would start by painting the trim white and leave the mantle natural for a bit to see if you like it, if not go ahead and paint it.