A floor plan would be helpful.

Find out if the wall is a supporting wall. If not, now is the time to take it out. I would remove the kitchen cabinets, etc and the wet bar, and start over planning an eat in kitchen.

The cabinets are all brand new so I am not sure we would have the funding to do all new cabinets and the stove and pantry are backed up to one of the walls. I think specifically the wall between the dining & eat-in would be the one we might be interested in removing or putting in a column? I'm not sure exactly what the options would be??

Do you think some bead board in the dining area or wainscotting would add a little more definition between the two spaces and maybe a nice rug in the formal dining?

I don't think it's really a bad space; appears rather functional. You have the pass-through and separation so that when in the dining room you don't need to see the pots and pans. I would suggest better lighting in the kitchen and if you don't need the ceiling fan, the kitchen isn't the best place for such. You could add some depth and drama in the dining area with a darker warm shade of paint. Is the floor vinyl? Once you move your things in, the place will not look so stark. You can make it work.

I think the best investment should be wood floors in all place. If you cannot take out the wall, you can put some art work and lighting and will look amazing.

Not vinyl, it is brand new tile. I really wanted hardwood at least in the living room area but it's new carpet and tile so I wasn't sure if it was worth it or not.

I'm sure the tile looks good in person. Nice neutral color. Carry on from there with some of the posted suggestions and I think you'll be pleased with the look.

You can leave the pillar if you are not sure. You can rip off the wall under the "window", because this wall won't stabilize anything and just leave the side walls of the window alone. . Or close the area to have storage and you don't have to put much other storage furniture in the rest of the house.

it looks to me like that wall might be holding up part of the vault, so i would definitely find out whether it's load bearing before going any further.

if you can't change it to a column and must leave the wall, i would take out the wet bar and turn it into a china cabinet with glass uppers that go to the grate up there.

i would leave the "window" area, and either enlarge it like linus said (if possible), or use that opening and creating some kind of extra bar-style counter area. it would be nice for formal dining when you don't want to crowd the table with all the foods/extra drinks, plus it could be used from either side.