It could still work, just don’t be surprised if she freaks out, runs up the stairs and pees on something in your bedroom.
Okay. It was hard to understand your post since you told me to “take everyone’s suggestion” when in fact it was my suggestion in the first place…
My daughter loved her easel, might be worth a try.
Just don’t tell her about spray paint whatever you do!
That’s the one I mentioned earlier. One side has a chalkboard, and the other is for paper. If I’m remembering correctly, both sides have a clip for paper.
Does she know how to get paper? Techniques aren’t obvious to kids–you need to teach her how to find you and how to ask, and she needs to feel confident that when she does that, it will work.
Throwing in my vote for the easel idea. My nieces have one, cleanup is super easy, and they love it. I guess it allows them to satisfy any “draw on a vertical surface!!” urges without resorting to architectural structures.
On the other hand (you know, if you want to go in a different direction), I drew on the walls as a kid. But it only happened once, because a day spent scrubbing can be a pretty big deterrant for a five-year old. And I tell ya, these days a sponge and a bucket of soapy water is much cheaper than one of those fancy easel things. 
Easels/white boards are a good idea, but echoing others who said have the budding artiste help clean the wall with you.
At 4 she should be more than capable of rubbing the Magic Eraser on the wall next to you. Granted her effectiveness at cleaning is likely to be limited, but the real point is to get her to connect drawing on the wall leads to unfun work of cleaning wall.
While my parents weren’t awful parents before I reached puberty, I can’t even imagine the shitstorm that would have ensued were I to draw on the walls. My parents were not “time-out” and “reason with the kid” type of people! 
There wouldn’t be any explaining, my hand would have been slapped every single time. My parents ran their house with Fear.
I like pretty much all of the suggestions in this thread. But I also think you should make her clean it with you. I just feel like otherwise you’re setting up for a lifetime of “Well, of course I knew that” every time she makes a mistake.
I did that with my daughter - just lined the walls with paper up to her usual drawing height. Ikea sell these huge rolls of paper very cheaply. Nothing else worked, and we did try everything, including sanctions; I’m not a laissez-faire parent. I once caught her drawing in her sleep.
Chalkboard paint is not the easiest to paint over, it’s quite expensive, and it’s only usable with chalk - anything else will mark it permanently, even moreso than on other surfaces. If she’s drawing on the wall next to her bed then you’ll end up with crushed chalk all over everything. I know this because, like I said, we tried everything.
She does have easy access to paper when she wants to draw, right? Ideally, without having to ask you for it every time.
As a former child, I do have to say that there is something sublimely awesome about drawing vertically. It allows you to get your whole being into the process. Stepping on tiptoe to get some detail at the top right is something I remember fondly. I don’t remember how old I was when I was drawing on walls, but I was old enough that I remember what I drew. (My favorite was a family portrait, with everyone as stick figures, including the dog. Everyone’s head, arms, and feet were the same, but the length of the stick figure was roughly proportional to their height. My father must have been about two feet.) Anyway, even as a relative grown up, in college, I would often go to an empty classroom, and puzzle out my math homework on the board. It’s a big space that just seems open to endless possibilities.
Anyway, the long and the short of this is that your child likes to draw, so I hope that one of the possibilities offered works out for you. Contain the drawing to one place, of course, but please don’t stifle this entirely. (I know that you don’t intend to.)
An advantage to paper is that you can keep some of the child’s work.
I have one of these too! She is 18 now and will be starting college next fall. She a talented artist with a fan club at her old High School. Some of her teachers have framed homework assignments, notebook covers and hung in their classrooms. A pair of her decorated sneakes hang from a light fixture in the school entryway. When the custodian removed them, the faculty and students protested and he put them back up.
Her ADHD therapist says the the constant drawing on any and all surfaces is actually a coping mechanism for a racing mind. If her hands and eyes are occupied with drawing, it lets her brain focus on what is being said and taught.
I do remember an article from some parenting magazine from a parent with a similar problem. She designated the kid’s closet at a ‘draw all you want to’ zone. Every so often, she would repaint the closet to give the kid a clean ‘canvas’. It worked great for her.
It could be worse. Check out this Chris Miller story from National Lampoon.
How about you go to the Art store and buy a big roll of paper and line the walls in her room with them?
What MissesA said.
She may also, as someone else mentioned, get WAY into having an easel
Whatever you do, encourage her to develop her gift
The only thing that I’ve found is supervised drawing time. I have a four and a two year old. I’ve tried giving them as much paper to draw/color on to keep them busy, but if left unsupervised the colors always ended up somewhere else - couches/walls/clothes.
The whiteboards and such are a good idea, but I would fear the same results. I can only say to try and keep them out of reach and setup times to sit and draw with them.
My nearly three year old has graffitti-ed the entire house. Every wall, all furnishings, mirrors, doors, floors, tiles, cabinets and my special favourite, the radiators which she did with wax crayon, while they were hot (very theraputic as it turns out…).
She did it over a period of months, in quick bursts, conjuring markers from nowhere. At one point I took everything away, anything you could write with was locked up. She became miserable and on the second day took to decorating the glass door with strawberry yoghurt and chocolate pudding.
We got her an easel which really helped and playground chalks for drawing on paving stones outside. The next great discovery was Crayola Magic pens which only work on Crayola paper, everywhere else they leave a wet line which dries invisibly. Yes they are quite expensive but they seem to last forever and the paper is replaceable. We keep these especially for restaurants etc now. We only buy washable markers and they are great, they really come off of her, clothing and walls with just a little water.
She has a big box of markers, pencils and pens as well as a good supply of notebooks, scrap paper and rolls of newsprint.
She’s got better, but will draw on any paper she finds, so important paper-work and letters have to be kept on top of the fridge. One thing she does love is to paint with water, using a fine brush and watch it evaporate in the sun. Now it is colder she likes to paint with water inside. I can live with that, YMMV.
She spends hours playing with colour and drawing, she also grabs a pen and paper if she is really upset and calms herself down by colouring.
I’m putting off redecorating though, until it really is all over (she has the occasional go at a wall or furniture, mostly for effect now I think), or perhaps until she can do it herself
Ours is a fan of “helping” with our half finished crosswords. Erasers don’t last long around here.
Mr. Clean Magic erasers are the 20th century’s greatest invention. Sharpie comes off with alcohol. Paint will cover anything.
Part of what your seening is an inability to control the impulse to draw. This could be something that will develop over time. The best you can do for yourself and your artist is damage control. Soon your creative baby will be moving across the country to college, making poor food choices, forgetting her coat, and possibly talking to strangers! (sob, sniffle, worry, worry)
I forgot about playground chalks, but I had a lot of fun with them. My daughter also had a lot of fun with them. I liked them on a chalkboard, but drawing on the concrete outside was the most fun. White is OK…but spring for the big bucket of colored chalks, the thick ones, and maybe invite a friend or two over. Or get out there yourself, it could be great quality time.