Love the wood stove!
I don't know about the vinyl flooring--but I would keep it simple, maybe just large squares. Then I would add a large area rug that would warm up the space--maybe about 10x12'--centered in front of the wood stove. I would mount the tv on the wall with a long low bench underneath, and find a small armchair or rocker to the right of the WS.
Do you use the piano? If not, I would put a small round table there with 4 chairs--great for games, or snacks, or socializing.
One of the simplest changes is paint: I would paint all the walls and brick the same colour--I think that would unify the room--so you don't have so many patterns going on. Again--I'd probably keep it light--maybe a light color from the area rug you choose. You could jazz up the bar area with some bright colors--maybe just paint it red (like your new sofa) and hang a funky light!
(a few ideas below...)

Thanks so much! Should I paint the bottom bricks the same color too?

I would not paint the bricks. Just the walls.

yes--I agree with eztia

The vinyl plank flooring called Allure is really great in the basement. It was so easy to install. It's basically linoleum but would work well with what you have here.