PS This is an in-between stage bathroom which will be turned into a closet someday and a huge master bathroom added onto this, so I don't want to spend a lot of money on it. I need something to look good for 5 years.

I would paint the bathroom mocha, the cabinets the deep blue in picture and add glass knobs. Replacing the counter top to white will not cost very much and will make all the difference for you to enjoy for the next five years. Replace mirror and centre over sink, remove stars on ceiling and change blinds to more up to date style. I would paint your bedroom blue or a light mocha so both rooms work well and it has a more up to date feel.
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I like the color combo in the pictures you posted- thanks!

Another budget friendly idea is Rustoleum countertop transformations. You could get rid of that green and choose any other color you like. As far as the rest if the color scheme goes, it's just up to your taste. The dark moulding at the ceiling line would look nice painted white and some simple fabric cornice boards over the windows would soften them. I would make them myself with a styrofoam kit and select the fabric from my local fabric store. In fact, I would pull the wall color from the fabric.

Are you changing the bedroom at all?

I am getting rid of the stars in the bedroom, but if I do paint the bedroom that leads to the window seat which leads to the hallway which leads to the breakfast room and so on. For now, I am sticking to the bathroom. The problem with the counter is that I have a tackle box for a make up kit, which would scratch the faux counter top :( I am however going to add molding to cover up the wallpaper border in the bathroom.

PS The bedroom carpet is a very expensive wool carpet installed by previous owners and until I can get new wood floors- the carpet stays- tulips and all.

The burgundy and black mantel (due to carpet) are fixtures, so let's discuss the rest. I suggest a gray that isn't blue for the bath - a neutral charcoal. Look at bm gray - a classic charcoal Yes, change the top - that will give you a big relief. See below for color ideas ..
Given the colors I see, the burgundy/cranberry has not been well balanced by that bright white. Since you have to paint out the gold stars anyway,
Shift all the white in the bedroom (and the walls of the bathroom) to off white / buff / linen tones - something historic (since you are rocking that look with the carpet and wainscot - in bedroom, I like
bm elmira white
http://www.benjaminmoore.com/en-us/paint-color/elmirawhite
You can do a creamier white on the trim and doors if you like, but I think unifying all (except the ceiing) with elmira will give you the most high end look. It will still look great against a white ceiling but will play much nicer with the burgundy
In the bath, go one half shade deeper on walls to bm jute - much lighter than you have now, but will shift from the bedroom to give more contrast to the white fixtures . . .great with the charcoal vanity, and you can easily go either buff/stone or pure white for the vanity top . . . easy to reuse in just a few years.
If you prefer to introduce a blue gray on the vanity, look at bm brewster gray

Libradesign is right on with the color palette. The burgundy is fighting with the white and toning down the contrast will make it flow much better. Charcoal/jute/white combo would rock the bathroom.

When the gold stars go, the gold art should come down and also the faux tree. I would try to lighten up the color in the room with new art/accents and bedding. Take a look at this:

gold stars are now history

ps- the charcoal would be a great look in the bathroom with a paler version in the bedroom. The tree was removed a while ago. Adding crown molding this week to bathroom, and looking for new countertop, with new sink.

Are you changing the mirror? Since you're adding crown molding you could get a plain mirror and frame it out with complementary molding. I have seen this done and it looks very nice.

have my eye on a mirror at home depot- will get it after a friend puts in a new counter and sink.