Do you have any photos of the kitchen and open area?

Light is important for most over 50. Task lights above the counter and muted light ( as a chandelier with dimmer switch) above the table is a possibility for your design

In a small open plan like this, the table rarely ends up staying where,you plan it to go. You can always swag a pendant, but recessed are also an option. Wall sconces are even a safer bet, but may not be enough light all by themselves (add some recessed too). The island is always a good place for pendants if it is stationary.

Thank you so much for everyone's comments and examples so far. I've attached the apartment layout as a reference. I'm still looking for the perfect lighting fixtures for the apartment.

It's going to be in the other half of a barn style building I'm doing for my photography studio. I'm going a little more modern for it, but with the nod to the 30-acre farm it's located on. I guess the best way I've come up to describe it is industrial farmhouse.

To give you an idea of the aesthetic, the building will be a light gray stained board and batten cedar siding with a dark gray metal roof, and the interior will be all polished gray concrete floors with flat fronted, frameless maple cabinetry. The kitchen island will be a dark gray stain, and the wall cabinets a pickled white wash (as long as I can get it not to go pinkish). The counters will be a steel gray granite in a satin finish, and a white subway tile back splash. The bathroom will have a zero entry walk in shower with a doorless, frameless glass separator, and a floating vanity. Not sure yet if I'm going to do the vanity in a dark stain with light counters in the bathroom or a light stain and carry over the dark granite from the kitchen yet.

Here's my ideabook on the project so far if you'd like to see all my inspiration:
http://www.houzz.com/ideabooks/13413245/thumbs/guest-house-studio

Both the island and the dining table should have functional lighting overhead, preferably suspended fixtures for interest. Sconces for ambient lighting would be optional in a small space.

What I find in this type of a layout, is that normally the table ends up where the red circle is. This provides better traffic flow. When it is necessary to extend the table, it would be where the green oval is. This means that the center of the table changes based on the use. To always center it on the outside door just creates an awkward traffic pattern and the table will soon be moved out of the way no matter where the light is. My scribbles are only to give you an idea of what I am referring to and not exactly accurate. The point is that even if the table only gets shoved over six inches, it won't look right. I would suggest that if you go the pendant rout, you just leave plenty of wire in the ceiling without a box through the sheetrock until everything else is finished and the table is there for a few weeks of living with it.

Fred, I hadn't even thought about a circular table moved closer to the pantry. I just thought I'd do a rectangular table across from the island, but then there's all that dead space near the pantry. Thank you for pointing that out. Now maybe I'll install a different type door in the pantry so they won't take so much space to open. I think your idea of waiting to sheet rock it in until we figure out were there table works best is spot on too.