How do I close up my fireplace without creating an eyesore?

Hello Sue! One of the first things you must do is seal your chimney so you don't have cold air and rain moving in. We fit a large piece of Styrofoam into the opening of the chimney and then made a chimney cap from treated wood and put it over the chimney. We painted the wood with waterproof deck paint/stain. You can also have a tin cover made at a local plumbing shop who make their own furnace runs. This will give you some energy savings from cold air coming down the chimney into your home, keep rain water from running down the chimney, and critters from moving in.

https://homeguides.sfgate.com/close-unused-chimney-30120.html

Here's some great decorating ideas for you too!

https://freshome.com/2012/11/14/10-creative-ways-to-decorate-your-non-working-fireplace

Hi ! First close the flue ... Then cut a piece of insulation board and fit it in the area leading up to the chimney , if you have enough room put 2 or three pieces for added insulation. Paint the bottom either black or the color of your brick . Now decorate the inside of your fireplace with logs , battery operated candles , or a basket of fake flowers ...

You could close the flue then clean out the fire area. Then you could put decor items in there such as a flameless candle grouping, large basket to hold a blanket, or some other item.

You can even add a plug like this:

https://www.amazon.com/Flueblocker-Rectangle-Chimney-Sheep-Plug/dp/B00G48EU12/ref=asc_df_B00G48EU12/?tag=hyprod-20&linkCode=df0&hvadid=194003459169&hvpos=1o4&hvnetw=g&hvrand=11730068891078576599&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9012555&hvtargid=pla-312625336257&psc=1

You have good advice for closing it off. If you still want to have a fireplace that burns perhaps you could afford a set of gas logs. We had them for a long while. They ran on propane because we didn't have natural gas. They did not need to be vented and provided instant heat. We cheaped out and didn't get the remote controlled set and I wouldn't do that again. In a different house we had a seal gas log set. That one did require that we run pipe through the old chimney it also had a remote control.