The tile doesn't look that awful to me. Looks like basic brown floor tile. Will the hardwood be an improvement? It will still be brown.

I would get a new lighter, not brown counter, change out the lights and mirror, paint a lighter color, and call it a day. May some fun art above the toilet or on the long wall.

If you stick with a curtain at the shower make sure they go to the ceiling and use a vinyl curtain on the inside track to repell the water.

Everything in your bathroom looks good with all the other items, but if I just wanted to spend money for a very generalized “update” I’d scape the ceiling, I’d replace the mirror/light, or at the least replace bulbs when they burn out because neglected easy tasks will always make everything look neglected. I’d also install a shower curtain rod instead of using a tension rod.

It's a nice space to work with and the tile looks pretty good! Consider updating the vanity countertop, perhaps a soft Corian in a solid color with backsplash that complements the shower tile, and switch to an undermount rectangle sink. Paint the vanity a soft shade. Replace vanity lighting and get a smaller mirror. Wall color can be decided after updates are known.

I like your tile floor. It’s carefree and attractive. Have you thought of adding a very long runner rug in front of the vanity? It doesn’t need to be very wide, but it could add some much needed color/softness to the room. Then just use the little rug we see only when you step out wet, then hang it up somewhere. Or drape it on the edge of the tub which could be out of sight if you add real curtains to the tub as suggested by Beverly.

In addition:

Remove the extra toilet paper from the top of the toilet and buy a holder that sits on the floor.

Lower the shelf over the toilet and put artwork above it. As suggested, artwork on the wall where the towels reside as well.

Add a washable runner(lots of places sell them now) - buy 2!