can you post a pic? so much easier if we know what you're dealing with

post an overall pic of the room, and the current light fixture.

(and you could do a larger fixture with 3-4 bulbs in. would that work? they're easy enough to switch out fixtures)

for instance, any of these would work in your room. or something similar to it. you want something with at least a 2' drop and enough lights to work in the space.

There are many lights with multiple bulbs now with LED. Look into more contemporary track lighting-the monorail systems even allow for combining spotlights as well as pendants. You should also make sure you use table/floor lamps as well. As for the fan issue, could you use a cool floor/table fan? I agree that combining fan/light will probably not give enough light.

What’s your budget? Layered lighting is your answer. I need photos and locations of wall and floor plugs. Then I can develop a good plan.

An electrician can put LED pots where you want them with very little problems and they can all run off that single curcuit. Lighting in any room but especially LR needs layering so the pot lights are only one layer, then you add floor lamps, table lamps , maybe wall sconces depending on your decor. I think it is not appropriate to bad mouth anyone on the forum and lighting is a personal choice so maybe the old owners did not require pot lights . IMO pot lights are kind of useless with 12’ ceilings . .

Welp, you did say the old owner was cheap for not putting in can lighting perhaps you should afford it now? I am thinking they may have other reasons they didn't, so without seeing the space, it is very hard to tell.

1. Track lighting ( modern LED small heads and come in several finishes.)

2. Tech rail lighting.

Those are the only alternatives to a chandelier or fan. Ps, a fanlight would never get your room lit up. A Chandelier you could drop low enough to give room light.

But Table and floor lamps are much better for functional light as you can get the light right where you need it.

Thanks for the feedback so far! Here are some photos - we're only just starting to move in so the future TV wall is just a makeshift temporary set up and everything is still a mess and unboxing. There are 2 outlets on the TV wall as well as 2 on the window wall. There are plenty of outlets in all corners, flanking the fireplace - so table and floor lamps would work but not great as a single broad lighting solution (like if I wanted to light and dim everything from one switch.. Most every example photo above posted was with plentiful natural light. Noted, that a fan light won't cut it - but a chandelier might.... That's probably the most affordable approach. Then supplement with floor lamps I guess. Track and tech lighting is probably a bit too techy looking but I like the idea of getting multiple lights. Since there is no eyeball spot for the fireplace maybe a small track for that could work, as one part of the whole.

what's all the plate covers in the ceiling? are you sure those aren't holes for recessed lights? Take off one of those covers. It looks like the wires were run, but previous owner didn't install the actual lights? (and by code, he can't cover up any live connections with drywall. hence, the covers)

if the hook ups are there, that's 75% of the work. call in an electrician.

The covers you see are fire sprinklers (we are in Northern CA Bay area) messing with one might set them all off so I wouldn't recommend it. :-)

oh my, well, scratch that! They looked just like plate covers!

5? for that one small area?

do they pop out of the ceiling? very odd looking

are all of the others speakers?

I mean, they did a number on this ceiling. All of this and they couldn't do a few lights??? very strange

i'd still call in an electrician. if wires are there for the speakers, then doing the lights shouldn't be too difficult. at least do one fixture dead center.

They may have had a ceiling fan or useful light but took it when they moved?

With 12' ceilings, you could hide wiring beneath a hollow wood grid the same color as the ceiling.

Coffered ceilings:

https://www.google.com/search?q=coffered+ceilings&client=firefox-b-1-d&source=lnms&tbm=isch&sa=X&ved=2ahUKEwikkcWXkunoAhVLheAKHeaUCMwQ_AUoAXoECA0QAw&biw=1366&bih=654

You could choose a design that suits the size of your room and your purpose.

If you turn off the water supply to the entire house and drain the water from the pipes first, you could risk removing the covers of the items in the ceiling. Make sure that the person doing this knows what they're doing ... not just guessing.

You have a nice room.
Candice Olsen back in the day did a house with a plaster ceiling so no overhead light?
She did a large reflective chandelier from the ceiling.
Then did wall sconces ( you can use plug in wall sconces and get cord covers for cords to eaten them up) on the sofa wall, a sofa table behind another sofa with a pair of lamps, a pair of lamps on the tv console, and a reading chair in a corner with a floor lamp. A total of three pairs of lamps, a chandelier hung at the right height( hung 60-65 “ above floor for 8 foot ceiling, the go up 3 inches for each foot above 8 feet. Hang bottom 72-77 inches from floor with 12 foot ceilings?. Good luck!

They did you a favor by not using can lights in a family room. Installing LED can lights will make the room feel like an operating room. Get a large chandelier and supplement with floor lamps, table lamps and picture lamps. It will feel so much more cozy and inviting than overhead lighting.

If you want to light and dim lamps from one switch have them set up on an app. My niece uses Savant, we just use Alexa with smart plugs.

track lighting does not have to be "techy", just go all white and have it blend away. or Bronze and have it an accent.

You have pot lights and what looks like electrical for many more what exactly is your issue, spend a few bucks or learn how to DIY those pot light hook ups. I do not think those are sprinkler heads

I will say this, that room is not that big, and I feel like you can absolutely use a chandelier in here, something beautiful to complement the view, but you also could easily get away with lamps on smart plugs as well.

Thanks all - I think the **chandelier** is going to be the first step and primary light source - so we will start with this and see what else is needed. A picture light over the fireplace will add - as will floor lamps - or maybe even go retro and do some up-lights!

Even though this was answered before - for the non-believers here is more evidence that those "outlets" are sprinklers. :-D

Even in the garage - right next to the light fixture!