If you are like me who cannot tackle the remodel on one big project expense, I would start with your breakfast table nook. Then I suggest working on the cabinets, and lastly changing the tile wall with or without counter top/sink update. An update of the faucet at the start won't be too much expense either. I am assuming you're not fond of the blue tile - wanting it to be in off/ white or grey tiles eventually. If you absolutely cannot live with the blue tile while progressing with the project, I suggest painting it like several commentators suggested as a temporary fix - just to get the pain out from looking at it :{) Otherwise, I suggest to leave it alone and save your money, time and effort. For the breakfast nook, I think additional storage is always an advantage like two commentators suggested for your wall by your table - using clean line metal/steel brackets and white shelves and wall painted with light cool grey in your ideabook. You can display not only kitchen items but also some artwork on the shelves to make it look uncluttered. I also like your posted ideabook for a bar style chair and table (Mal Corboy) but with low open back chairs for airy look (Kelley Gardner.) Assuming it is safe to cover your radiator panel (sic maybe - not sure of term), the wall end of table can be opened with cabinet doors on both sides or at least the one facing the boiler side. (Pls refer to 1st image.) For the cabinets, I suggest going up to the ceiling even above the window/sink - using simple panel doors with long sleek hardware just like Merry Powell suggested. Going up means less wall tile to change later in the project - an added advantage. I also think that painting the lower cabinet that same light grey as your wall also looks pretty just like in your Cucinabella Bella choice in your ideabook while top cabinets are in white. Just be careful which white shade you choose. A true off-white may not look good with the grey you posted in your ideabook. Your boiler corner can have its own two-door corner cabinet or 4-door cabinet if you paint the lower ones grey. (Pls refer to 2nd image). I am attaching images with edits using my unglamorous graphic 'editor' - excuse the roughness ;) I also included images posted in your ideabook mixed with my added images. May be a lot of work but have fun while doing it. I'm sure it will be much better looking each step you take.

I agree with everything said so far. Would suggest you get built in book shelvers on both sides of fireplace, lift tv into a slot it fits perfectly into (make sure you have power on both sides). Then it will disappear more rather than fight with fireplace as focal point. I am always disappointed with mirrors over fireplaces, they become dark, are to high to reflect much. Plus then you have three rectangles fighting for center stage. I'd say very colorful artwork instead. Wonder if you can reorient tv where the big chairs are so both tv and fireplace are addressed? Color, maybe you should decide on furniture first?

Paint the wood floor with a flooring paint. If you want to be creative, you can create your own special design. I've had painted wood floors in a previous home and everyone loved them. If you get tired of it, paint them a different color! Saves doing rip out and better for the environment! My floors held up well. I was surprised. I even did a faux marble floor for fun.

This is an old kitchen faucet and I would like to upgrade it but I have no idea what kind to look for! Please help!