Re: the basement stairs, I don't think it's the distance from the dining room, but that you have to walk through the mudroom to get to them. So for using them for storage, or if there's a utility space down there that makes it better to be near the garage etc, then the basement stairs are fine. Or, if you really want people to use them, open them up a bit with a half wall to the sitting room, and remove the door. If you need a door on the stairs, out it at the bottom. But, guests have to snake through the busy kitchen or mudroom to get to the sitting room. It looks like such a pleasant spot, but not for entertaining. Re: the L-stairs, does your fear of heights bother you standing at the top of the stairs, or only when there is nothing below you? If the latter, go ahead and don't have an "open-to-below". Upstairs, maybe a half wall? i like the way the L stairs empty at the bottom. And it's a much nicer view from the door: do you decorate for winter holidays? Imagining lights or garland on the railing, so pretty.

You should be able to do some kind of closet under there, with a pull-out at the lower end and maybe even a traditional closet for the rest, depending on measurements. You just need to keep enough studs for the structural integrity of the stairs themselves, so you don't want to yank it all out! As for color, just have the doors finished wood and paint them to match your trim (currently white). Then, whatever color you end up with for the other finishes in the entry, it will either match or be easy to repaint. Don't make everything contingent on making all the decisions at once or you'll pass out from overload.

I LOVE acm's solution! What is your biggest storage need? Perhaps, since you just moved in, you can wait until you need a place for something. No need to fill up space just because it's there. OTOH, I have under stair storage. I use it for seasonal things - artificial Christmas tree, hunting clothes - things that are in tubs and can be easily pulled out to get what we need, but only needs to be accessed a few times a year. If this is "prime real estate" in your home, you may want to use it for everyday use - vacuum cleaner, sports equipment, etc. Only you know what your needs are, and how the space relates to the house. Good luck, and let us know what you decide!

I have an under-stairs area in my basement. I have a few elfa drawer units from The Container Store where I store all kinds of things. They have ready-made ones, but you can also design your own, with the height, width, and number/depth drawers you need. Shorter ones go at the back. They all have wheels and it’s a hard-surface floor so they roll easily to get what I need. Some elfa accessories hang on the sides, too, like baskets and hook racks, for convenient extra storage. The Container Store has a “33% off“ sale on them in December-February.