Hoosier.

Can you show a picture of the rest of your kitchen so we can get an idea of style and features?

This should surprise no one:

Cabinets?

I have lots of long wall space like this. My smallest is 60", with the largest being 16' 10".

On a couple I am hanging floor to ceiling wall cabinets. In particular, my laundry room (72") where I will put my clothes. I have nothing but open bookshelves now.

In the kitchen, another 72", I'm creating a credenza -- or Hoosier, if you will! :)

These odd walls, no matter how big or small, create weird empty spaces. I'm making mine useful.

Figure out what would be the most functional and pleasing.

You could even create a Tansu type layout, which would leave wall space to hang artwork or something. I'm doing that in my MBR. Originally there was to be a fireplace, but being impoverished, maybe someday I'll hang a TV there or something. Again, functional.

Some ideas.

Here's the other side. These are older pics before the island was put in. I'm not in love with my kitchen, and after our addition, it is the next thing I want to tackle. I want something much brighter.

As you can see, I have no pantry, so that was my first thought for the empty wall. But it would have to be free-standing, or how can I work around those horrid baseboards?

Baseboard heaters can be moved. Ask a local HVAC person what it would entail and what it would cost. If it's too much to move it to the outside of a built in pantry, you could do cabinets with the heaters in the toe kick.

What do you need? Food storage, dish storage, storage for occasional/seasonal use items, a coffee/beverage/breakfast station, a craft or homework station, utility storage, pet supplies and feeding, seating space -- some combination or something else? Figure out what you want the space to do for you -- how it can add to what you do and how you use the whole space, then figuring out what to put on the wall will be much easier and more meaningful.

My sister has those baseboard heaters too. The custom cabinet maker built a wall oven unit and pantry on that wall. He built them on legs that match the cabinets. It was a first for him but he did a beautiful job. The wall has a wall oven with slotted cabinet above it (for cookie sheets, 9 x13 casserole pans, jelly roll pans, etc) and drawers below for more baking dishes, then 2 Pull Out pantry cabinets with plain cabinet above them, then a broom closet. It works well.

I wish I lived close to her so I could get a picture for you. The legs are tall enough that she stores a childs booster seat or sometimes a child's stepstool underneath the cabinets for when her grandchildren come. It is out of the way and yet close at hand for the kitchen table that is nearby.

In a perfect world, what I'd want would be this:

In reality, though, not sure how that would work. All because of those darned radiators. My BIL offered to build out the wall to make a pantry, but I'd have to move the rads.

Oh, just adding, we don't have a basement, so re-routing the heater would have to be through the walls? Is that possible?

Although we don't use it much for actual breakfast nooking, our design left us with an 8 x 6 deadend that butts up to the side of the refrigerator. In it we have an antique table with two wings that folds down to 1.25 feet deep, renovated pendant lighting fixture, antique chairs, and a fabulous wall for a single piece of art. On the short wall alongside it we will be putting a 5 foot wide bookshelf, which will be mostly used for books but it also will house a few display pieces.

When we have parties, we shorten up the light chain so people can walk under it. We open out the table and tuck the chairs around the back. It makes a fabulous hors d'oeuvres station or a drinks station and it keeps people away from the cooking area just when I need to be left alone.

The art wall can be seen from a long distance--we planned it to be our "ta-dah!" spot and it's a funky counterpoint to the rest of the room. Currently, the table has a number of amarylis plants on it. In season we put other current flowers and, again, it allows me to have these things in the room but yet not in the room, the best of both when I'm busy in kitchen. In addition, the bookshelf houses my big collection of cookbooks. I can pull them out and lay them out on the table without intruding on the action in the kitchen itself. I sit there, researching, and the pile of disregarded books is later stacked up ready for reshelving without getting flour on them. I only take one into the actual cooking area.

We have run a number of heating ducts through cabinetry at the bottom of a wall. The bookshelf will have one running through it. We just extend the tin channel out to the outside of the cabinet. We've been using oak grates on the ones in our oak kitchen.

thanks for the ideas! I don't know why but whenever I put something out of the ordinary there, (like the desk that is there now) it feels so un-kitcheny. I even had a loveseat in there once, like a faux great room feel so people could sit and talk to me while I cooked (before we put the island in).
I think the problem is that I have 'pantry' stuck in my head since 1) I don't have one and 2) it seems like a logical spot for one!