what a cute area. what renovations, if any, will you tackling? Are you keeping the carpet on the stairs? If not, I would suggest removing it and seeing the wood treads are good enough to refinish. then I might tile the risers with something to match your hex floor (are you keeping that or replacing?)

A really nice chandelier would be another option, although the one there currently is fine.

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if you could get your treads finished in this gorgeous walnut shade and then do some type of tile (it doesn't have to be flashy. You could do a simple tile), it would really perk up that entry.

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Do not put a mirror on the basement door. Paint it white like the trim.

I think I would remove as much from the entry as possible and then create interesting "draws" to the adjoining spaces. Love Beth's idea for the stairs. That would be awesome. Definitely new chandelier in entry. Repaint of course and paint the detailing on stairs all the same white. I am torn on the entry tile. I usually don't want to remove original stuff. But I can see and black and white marble in this entry and then that concept being the stairway color palette. White walls, paint the radiator cover black so it disappears as much as possible. Paint the water supply to the radiator as close to background color as possible to make it disappear, or a metallic antique gold. Lots of possibilities. Door is fantastic. The red is distracting, so if you go black and white inside, paint the door glossy black with a brass kickplate and brass hardware.

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Agree, no mirror on the basement door.

And with removing the carpet on the stairs.