If you draw and measure BOTH spaces and how they relate to one another, add feet and inches for all? You will get a lot more help. That's walls, windows, the front door, , the column an where it is etc.

You aren't even showing a view from the kitchen.

If you have the floor plan from the house, with dimensions? Add that.

As to existing electrical ? Lack thereof? That is what electricians are for!

Before anything, it is draw and measure, feet and inches. Add it to a comment below as Jpeg , legible : ) and an actual plan can come your way.

In general, the TV would be in the room next to the kitchen, not in the one by the front door, but I agree with Jan that you haven't provided enough information for us to address your particular situation. I also agree with chispa that you can use rooms in any way that suits you. I have seen people switch their living room and dining rooms, or use their dining rooms for home offices or childrens' playrooms. When spaces are open and undefined it can be difficult to determine what you want. I suggest you provide more information so you will get better advice.

Based on the pics you posted we have no idea how the window area of the room connects to the fireplace area of the room.

Obviously you can mount a TV on the large wall and have seating placed to face the TV.

Here is the floor plan of the house. Purple dot is where the pillar is. 1 and 2 is where I am thinking to have the tv at. We overestimated the space and bought too big of a recliner and now we can’t fit it in our place if we have the tv at #1 (where plug and cable is available). I may have to return it and get a recliner loveseat.
Ideally I want the tv to be mount above the fireplace and not returning the current recliner but there is no plug outlet there. Also love to have advice on pick rug. We have a toddler and my husband really wants the white wool rug in the living room next to the kitchen. I think we need a washable rug there, please advise!

Thank you so much for respond so quickly!!

I usually prefer the TV in the space that does not have a FP but in this case the TV near the kitchen really make the most sense and the room at the front not for TV.

Why two family ( living ) rooms? How many people live in the house? we converted our family room ( previous owner ) into a spacious dining room.