Personally I'd keep the brick. It looks lovely, at least from this angle. And the arched brick fireplace looks like a smaller version of, or homage to, a classic Frank Lloyd Wright design.

Ditto the brick. Instead of painting the brick and fighting the arches, repaint the room in a medium shade of Terra Cotta or Wheat to capture the weight of the ceiling and brick. Add simple shelves to the arched openings. You might feature the inside of these two openings by installing something reflective like antiqued mirror or a distressed silver leaf wall paper. The add shelves and accent the rooms with an occasssional old pewter or mexican silver item (buckets, pitchers, etc.). By thinking of the entire space as old rural Italian or Mexican you'd have a he-- of a beautiful space. If you like these suggestions then you can add a primitive looking area rug, white or canvas slipcovered upholstery too. The pendant light over the table can be changed out for a pierced Silver lantern. Pedestal table in natural wood with some cane or pierced back chairs. Loose the fake greenery and hang a cool poster or painting with an image of a countryside to add a colorful "view" over the FP.

Not sure what is in the cut out above the right side, but I agree with Jeffrey Brooks. You don't say what your own personal style or that of your furnishings is, so I'd say leave it alone, add your stuff and re-post for further ideas on how to make it all work together.

Hi deco.......! I was talking about the arched recessed sections one either side of the FP.

Love the round feature! Keep it!!!
I don't think the brick looks bad at all, until you can do what you want....but if you want to paint it until then, paint it one of the colors that is in the ledge stone. Get a sample of your stone color you like and take it to the paint store for reference!

The brick fireplace is lovely as is just change the focal on the mantle-picture, art glass so many choices would be nice. It really is nice change the plant.

Thanks so much for your sharing your opinions. We are open to advice. An big thank you to Jeffrey Brooks, such a thoughtful response. Too bad we're not in NYC so we could hire you!

Honestly, our taste has been hindered by our budget. Call it a step above Ikea. My husband loves mid century modern / prairie, I love more contemporary. We both are warm and welcoming. We have a dog and a child so the decor has to be easy maintenance. We are not fussy/ tchotchke types. We love color - I love the colors of Mexican pottery and also the reflection of the pool and sky through the window.

We would love all the advice anyone cares to share! Thanks again.