How old is your house. If I get stuck I try to choose colors that would have been used when my house was built. Or you can go with those of a later remodel. For example I dont want an 1850's kitchen to match my house so Im pretending like it was remodeled in the 1920's. Still old but much more cook friendly. LOL. I see two ways to go with your bath. One would be to paint it a white that goes wth the tile. Then get your pops of color from your towels and accessories. Advantage would be easy redecorating. The other way would be to go with a contrasting color on the walls. You can go a little more crazy in a small room than you would in a large one. Lemon yellow, hot pink, cobalt blue, kelly green, cherry red, turquoise, apple green. If it were me I would use one of my accent colors from the adjacent room. That way it would go with the other room but not look like an extension.

A warm off white would look very nice and was my initial thought. It's often my first thought for wall colour these days and I hesitate to suggest it because I worry it's a cop out of some kind. :P Get a test sample jar/can of whatever you're considering and paint it on a few inexpensive art canvas boards so you can try it out on all walls. Take your time to see the colour throughout a sunny and gloomy day's light.

What does the rest of your bathroom look like? I’d do some nice wallpaper, and the rest just like you said. I’m no designer though. Depending on how far down the renovation road you want to go, perhaps consider replacing the floor tile to something more era appropriate? I think alot of bathrooms from this era had chrome (or something like it) hardware...but if you have original hardware that is brass, continue with that. I would think that the latches on the top cupboards will be an indication once you’ve got the paint off, whether the knobs etc should be brass or chrome(?) I’m not even sure whether you have to put the baking soda in...I’ve done it with and without and it’s worked both ways.

I like the suggestion from Kate to paint the walls a soft white. If you have enough wall space, I’d add artwork that includes the colors of your floor tiles.