If you plan on sitting in this main area reading a newspaper, I would add the recessed lights here as well. Add a dimmer to so you can get the softer light when and where you need it.

Downsouth, thanks for you ideas. I agree that I need to be able to read in this area. Since it is such a small room the only real seating is the sofa which will have recessed light above it. The sofa will be outside the tray area. The tray section will be over open floor. I'll try to post a floor plan tomorrow.

Ahhh, great that someone else likes the rope lights. I have the LED rope lights which will be on a dimmer to circle a room. I highly recocmmend the LEDs, which do not get hot.
And they last a long time.

And reading is important, even if it is just the TV Guide or the instruction manual for your electronic equipment.

Have you considered locating a couple of the recessed lights so they can give a down wall wash?

Most rope lights not very bright - if you need brightness, go with T5 or T8 fluorescent tubes. Newer LEDs can be brighter than they used to be though. In either case, carefully choose "color temperature" which ranges from 2700°K (warm like incandescent bulbs) to 3500°K (neutral or "bright white" like GE Reveal) or 5000°K or higher (cool, daylight) - this can make a huge difference in the feel of the room.

Be sure there's enough depth for the recessed cans you choose if you put them in the raised-ceiling area; deeper fixtures may not fit because they crash into the floor above. There are all sorts of shallow-ceiling recessed cans available if you need them.

Get good-quality dimmers and ballasts/drivers so it won't buzz or flicker when you dim them.

Thanks for the thoughts on the rope lights. I still haven't decided if I will do them or not. I have plenty of room to install cans but was just thinking that maybe I didn't need a lot of light in the center of the room.