How about a mirror and small entry way table for the larger of the two? Other ideas might be a decorative umbrella stand with a museum styled umbrella, or a coat rack. There are some very ornamental ones on the Joss and Main website.

Are they symmetrical? In other words are the alcoves the same size? If so, I'd keep it formal and symmetrical in design. Maybe purchase two small tables or cabinets that can fit inside the space. Then add a buffet type lamp (looks like you have outlets in each) and decorative framed mirrors. Another option is two large floor vases.

I think I'd remove the silly crown molding from the alcoves.

If they aren't symmetrical, I'd close them in and make them coat closets.

Closets.

Closets make sense to me.

Closets, or cabinets with glass above for display. Closets would be my first thought.

They are symmetrical. Closing them in seems like a lot of work for something I don't need. I have a large coat closet in the hallway. And another in the mudroom. So funny, I never noticed the plugs. Like the idea of mirrors, small table with a light. Would love some other opinions on styling. Just moved into this traditional home in Connecticut from Florida. Very different than what I'm use to.

Beautiful wainscoting! This could be a perfect location for extra storage or a mini mudroom since it's right off the entry.

If you don't want to close them in for closets, how about adding windows? That would ad a lot of natural light.

not awkward at all. i'd do small console tables in each, with either narrow mirrors or 'comparable' art, and a small lamp.

Love the idea of adding windows!

windows have to work with the outside too... how would such a window the right size for inside look on the exterior? i should think sorta small.

Closets:)

Should have been closets from the beginning

Perhaps a small bench in one and a chest in the other. With long narrow similar art in both. Whatever you do I would definitely remove those pieces of crown molding.

Don't overthink the spaces. Mirrors would be practical. If you don't find something right away, don't fret. The spaces are fine empty for now. I would start with a new rug and light fixture first.

Another closet vote!

Like those benches! Why don't visit some local shops and home boutiques and get some ideas from local artists and decorators since you are new to the region. Closets are redundant. More windows might and probably will affect the architecture of the house.

well, you need 2 of the same. try wayfair, you can search by exact measurements. mine are from pier 1.

I think the alcoves are meant to be decorative. I would have a carpenter build a top with glass inserts to match the top of the door; new side tables with lamps or mirrors or art. The electric outlets are meant to be used, and why would you want to look at 3 doors so close together when you have a closet.

I would not have matching anything. I would fill it with art or favorite photos in similar frames.

The closet idea is good, but if you don't want to do that, you can do mirror, consoles with art over them, a coat rack in one, and a bench in the other, etc. Here are some images from our portfolio to aid you:

May be something like this, with Paula Deen Round End Table from Masy's. The same Avalon End Tables from Wayfair for better price.

Alcoves with just lamps look empty.

Here is some inspiration

With semi circle console table

Really like this idea. Thank you!

Another idea to paint alcoves in darker color.