In our bath with brass doors I hung up a shower curtain to cover them up. Put on a tension rod in satin nickel.

Thanks... I actually already did that (I pulled the curtain back to show the brass for the pictures). :)

How much of a budget do you have?

Do you need doors on the tub or can you remove them and just use a shower curtain?

Laying new sheet vinyl floor is pretty simple and inexpensive.

I wouldn't paint the vanity, just change out the hardware and faucets.

Embrace the brass since it's making it's way back in. Paint the vanity and dark wood medicine cabinet a creamy white to lighten things up. Get a nice runner with color for in front of the sinks. Nothing wrong with your jewel tones. You just have to work with them.

Replace the towel bars with something in a antique brass finish.
Not sure if you are using all of them. If not remove the bars you are not using.

Check out HOUZZ for pictures of bathrooms with brass fixtures.

If you are crafty, I've seen posts online where bloggers have used Rub and Buff to make old-fashioned shiny brass look like the new-style aged brass. Instead of hiding your brass accents, perhaps you could make them less shiny.

I agree that painting the vanity a cream color would help lighten up the room. in my old house, I painted the vanity using the following advice from igloochic:

This is exactly what I use:

Primer
Sherwin Williams PrepRite ProBlock Interior Exterior Seals and Bonds, Latex primer (it's the most expensive...but if you don't like sanding or using chemicals to prep, this is the stuff for you!). I've never had to sand or strip first using this on the worst shiny stuff.

Paint
Sherwin Williams Exterior All Surface Glass Enamel
Code IFC411X
Woodsy Brown 100% mix formula 2924 (color code)
They use Acrylic Latex HIGH GLOSS Ultradeep base 6403-25932
Code A41T00204

Do not take a less glossy finish. This finish dries HARD and rich :) (There's a man joke in there somewhere but I'll avoid making it)

I use one coat primer and let it dry a day at least, then two coats (one day between at least) of paint with a good Purdy brush (which is important). With just one coat the grain still effects the paint, but with the two on top of the primer you get that nice smooth look :)

I'm a paint freak, so forgive me for saying this if you know. Don't use rollers for wood. I like a 1 1/2 inch and a 2 1/2 or 3" brush at the most. The smaller works well on the small areas so you don't drip or oversmear the sides of the project."

In my new house, I'm using these aged brass knobs:

I think the green trim and tile is lovely. Usually this kind of color looks dated from what I've seen but yours is so rich looking, I can only see the loveliness. (of course I'm not a designer but just sayin...)

I've been thinking about your bathroom. I think you ought to put as much off-white/cream in that room as you can to lighten it up.

Paint the vanity and the medicine cabinet off-white/cream.

Are shutters for the window within your budget? If so, install off-white/cream plantation shutters at the window. If they are not in your budget, consider plantation blinds in the same color. Or a roman shade also in off-white or cream.

Put one or two off-white/cream rugs on the floor, similar to these:

Find some other place to store your curling irons and extra TP. I'm afraid in their current location they are blocking some of the light and causing the room to look dark. Consider changing your lightbulbs to GE Reveal in the highest wattage your light fixtures are rated for.

You'll have to get accessory advice from the others on this forum. I'm no good at it.