It looks like the dining room? And you’ve got it set up as a dining room, right? What’s your budget?

I like more open rooms, so I’d take out those half walls.

Depending on the budget, I might embrace it’s dining room-ness, and put the sewing machine elsewhere. Instead of the China hutch, it would be nice to build in that wall with counter height cabinets, to make a buffet server, and provide closed up, neater looking storage.

Your really weird room is a dining room?

What do your parents want to do with it?

I would not take out the half walls as they keep people from tripping on the step down. Is the problem that your parents don't use the dining room or they keep things that don't belong in a dining room there like the sewing machine?

Is the ceiling the same height as that of any/all the adjoining rooms -- or just the floor that is higher?

Is this a corner room -- outside walls?

Have you checked beneath the flooring to see if there is an obvious reason the room was built with a higher floor?

Which room -- this "bonus" room or the living room -- has the same floor and ceiling height as the rooms in the rest of the house; which room floor is different from all the rest?

Can you post a floor plan to show all the nearby rooms; is there any chance that that one or the other room -- such as the living room -- might once have been either a porch or garage?

The eating AREA in the kitchen is the informal dining area. The room next to the living room is the formal dining room. You can use it for whatever purpose you like-TV room, library, office, music room...

Card table/games, reading/exercise, hot tub!

You could have it be a lounge room/reading room, a library, an office, or maybe a game room?

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Add a door for mudroom? Media room.

Rather than removing the pony walls, you might consider swapping them out for floor to ceiling shelving -- placing their base (whichever room floor ) where taking up a foot or so of space to build them would be best.

http://www.thematador.us/bookcase-floor-to-ceiling/floor-to-ceiling-bookcase-room-divider-home-design-ideasfloor-corner-shelving-units-shelves-unit/

It looks like a formal dining room. Not weird, used to be very common for people to want formal dining rooms and formal living rooms, but in more present times they are often underutilized as such. The other space in the kitchen for eating would be considered the dining nook, breakfast area - the more casual eating space.

If it is not being used as a dining room, I'd just turn it into a den/lounge/library room or something of that nature. Like a smaller sitting room for reading, games, etc.