Would the HOA allow you to change the door to something with more glass? Google 'glass front doors' to see what there is to offer

Better lighting will definitely help. And a new door.

Paint the door a bright color, hang colorful prints up the stairwell.

Since it's an apartment, I'm guessing there's not much you will be allowed to do.

First, I would clean the carpet (Ideally, call someone in to do it as stairs are a beast to do and it will be worth the money).

You don't have any width to do much here, so what about something like this that you can wrap around the door/wall and and up the stairs a little? They're vinyl decals and easy to remove and are kind of cute. My favorite color-of-the-day is red, so I would say have it done in red to brighten up the area. I would also get a red door mat that coves in front of the door..

This one: https://www.amazon.com/Anti-Bacterial-Non-Skid-Interior-Decorative-Home/dp/B00TMAONLQ/ref=sr_1_21?s=lawn-garden&ie=UTF8&qid=1503778753&sr=1-21&refinements=p_n_feature_twenty_browse-bin%3A2972994011

is thin enough that the door won't catch on.

I had a front door exactly like that, although it opens into my living room and not a stairwell. I switched it for a 3/4 lite and it transformed my space. It was probably the best fix I've ever done at my house. I have a roller blind for privacy at night. It rolls completely out of the way.

If you open the door and see what kind of light you get, it's like that with a full or 3/4 door.

I also agree with painting the inside of your door a bright color and/or better lighting. I hate having to have a light on when it's a perfectly sunny day.

HI -- Put some rope LED lights on the ridge on each side of the stairs . You can even get the color changing ones .

Here's a quick fix with the SW paint program. It doesn't look like lighter but it looks more cheerful.

Hang mirrors and art on the wall.

.

There are battery operated picture lights. Perhaps 1 or two mounted on the soffit over the stairs would light the space bit.. They start at about $30 or so and some have remotes.

LED Battery Operated Picture Light with Remote Control, Dorado Bronze · More Info

Great idea carrellhouse! I may use it for a stairway I would like brighter.

Do you live in CT? My son's entry is exactly like this! Since it's a rental, there is really very little - read that "nothing" - that can be done. It needs sconces on either side, or at least one side of the door, and that involves an electrician and I doubt the property management company would allow it. The good thing is that only you notice it.

How about stick on stair lights--they'd add some brightness and then art work up the wall would provide interest.

The problem with painting the door is that it will only be seen leaving your apartment. You want things to look cheerful coming in.

I agree with better lighting and some wall art. As people walk up the stairs, they have something to look at other than the stairs.