I think that will be fine. Do 4" LEDs and put them on dimmers.

Thanks! I think thats our current plan and its nice to hear from another person. We are lightening the room with nordic floors and a a off white creme wall color. What do you think for the fire place? We were thinking of white washing it?

White wash it, remove the black/gold screen, and add a natural wood mantle to matche the beams.

Something like this:

But even this is a little too opaque. Do a lighter wash to have more of the brick show through.

Contrary to what is commonly DIYed, placing a grid of recessed lights in a seated, relaxing room with a somewhat static furniture layout is not very pleasing. Look at where the lights you intend on placing land - 2 on the long couch person's heads, 2 providing glare on the tv, 1 on the close chair person's knee, 1 on the reclining chair person's foot, and 1 highlighting the door.

Instead, a Living/Family room should be layered lighting, so here just a couple recessed accenting the fireplace and continuing with floor/table lamps at human head height.

Great ideas. What did you mean 2 providing glare on the tv. Wouldn’t I not want glare?

You don't want lights reflecting into or messing up you seeing the picture clearly on the tv.

I wouldn't use any recessed lighting in the room. A combination of table and floor lamps, perhaps a sconce or two, uplighting on plants, and picture lighting on artwork will be sufficient. Maybe eyeballs directed toward the fireplace. And everything on dimmer switches.

Too many ceiling lights, especially LEDs, make the room look like an operating room.

If the beams are hollow you can probably fish electrical through and install recessed downlights in the beams. However, the room should have multiple layers of lighting which includes, table and or floor lamps.