What beautiful doors! Since you have a heating register immediately to the left of your door, I would put nothing there. I believe that your entrance rug is nice, but not appropriate to that lovely space. Something more bold, perhaps with a traditional Persian pattern? Something that would compliment the Victorian hall stand. Adding color rather than things to the area is where I would start.

I would move the hall tree to the side wall and I would place a round pedestal table in the stairway corner where the hall tree currently sits. A lamp, vase of flowers and well framed piece of art on the wall to finish it off.

Rough mock up

Beautiful entry! Do you need something functional by the doors or simply decorative? What about a small entry table or beautiful umbrella stand with art above it on that left inside wall? If you have an outlet on that wall, you could place a pretty lamp on the table. The rug is lovely but doesn't seem to belong here. I agree with ptreckel's suggestion. Something colourful and traditional would look fabulous. For the hall tree, I sometimes see them styled with beautiful hats, a bag and a plant on the seat. Really depends on your style. Google "antique hall tree" for ideas. You'll find plenty of pics on Pinterest. See what resonates with you. Here are entryway ideas on Houzz.

Awesome! So, so helpful!

If it’s just for decor, how about a tall plant in a beautiful planter by the door?