Help me with your picture, what angle am I looking at?

This is looking in through the dinette area and family room from the living room.

The last kitchen I did, I used a cut out instead of just building a half wall. Cabinets were installed on on the bottom with a pot light over the counter( pendants look good too). I kept bar ingredients in this area and had the full counter to mix, blend and create. It's always nice to have a full counter with no cabinets overhead. This bar space was on the kitchen side but my pass through went into the dining area. Either side can work as long as the flow of dining furniture is not a problem. Cabinets would be cheaper than buying a bar type furniture piece. Bottom line, I never regretted putting that bar space in!

If adding wet bar do on family rm side with shelves.

Ok, so now knowing the space, you have the perfect setting! It will be used and you won't regret it. I myself was happier doing a window cut out versus only a half wall because it seemed to keep the spaces defined more. My cutout opening was just above counter height to about 6 feet. I liked having the option of adding a shutter or something decorative to block the space if I needed a change. At one point I had a stained glass panel in the opening and could remove it from hooks if I wanted to talk to people on the other side while entertaining. Just ideas!

I think you have to think about how you use the space. Where does your company usually end up? Keeping it in the less formal area keeps your formal living area clean.

If you did a half wall, shelves would not fit, but a pass through gives you room and keeps people connected. It's a matter of preferences now.

Do you entertain a lot? What would you use the wet bar for? Have you had one in the past? If you have cocktail hour every day, yes, you might like one. Remember it's one more area to clean.

I agree with Aa Maintenance cabinets are very useful. We have a few blogs that could help with the process.
http://budgetmybuild.co/kitchen-design/tips-perfect-kitchen-cabinets/
http://budgetmybuild.co/design-budget/purchasing-cabinets/
Lowes also has alot of ideas for cabinets.
http://www.lowes.com/ideas-how-tos/kitchen-and-dining/_/N-2zbjj/npc