We are looking to mount our tv over our fireplace on the first floor (no basement) but a few issues: 1. It's a freestanding fireplace (see photo) and 2. There isn't a cable box. I'm not thrilled about the idea of running cable under the carpet. What would be our other options?
I am assuming you're talking about pulling two types of cables there, potentially three - power, coax and CAT5/6. The little complication there is that power and low voltage require separate paths, i.e. each requiring their own access holes through top / bottom plates or the walls you're going through, separated by at least 6".
There's an obvious consideration: do you own the place or rent it? You're obviously more flexible with your options if you own, and some things you do may simply only be justifiable if it's a solution you will use for few years.
What kind of a fireplace is it, gas? There may be a blower motor in it, so there may be power already there, you may be able to connect the TV power outlet to it. The low voltage connections are rather easier, not the least because you may be able to eliminate the need for them by buying a Smart WiFi TV.
If you are determined to pull cables, investigate how the fireplace's chase is built. It may be worth cutting an access hole to have a closer look. There may be enough space in it (as far away from the flue as possible) to pull a cable up into the attic and then come down to the distribution point, wherever it is (garage?). It may also be possible to use the wall to come up, between the floor joists and into the second floor's wall, then up into the attic again. This will require cutting more access holes and may not work if your walls don't stack or too far away from one another, requiring horizontal runs on the second floor in a place where there's no access.
In any event, this is going to be a huge project that can end up with your TV sitting too high for your liking anyways. Before attempting something like this, I would ponder very hard about an alternative place for the TV and considering mounting a painting above that fireplace instead.
I hope to hear what you eventually end up doing, perhaps you can update us when your project comes to completion, one way or another.