Thanks. I have seen the other picture of the space behind the chairs as well. You have a difficult room to work with. Also, have you considered the ideal viewing distance to your new TV. You can find this online. You may want to take this into account as well when placing your furniture. With a larger TV, you will need to sit a larger distance away from it.
However, let's get into possible solutions for placement and stands. Do keep in mind that none of them will be perfect.
The current layout might be the best for this large couch you have. In that case, I would put the TV flat against the back wall. One person can view it from the couch and another from the chair. A normal size for a TV stand would 6 to 12 inches wider than the TV on either side. With this layout a regular stand may infringe on the sitting space of your couch, so you may have to go with a shorter stand. Make sure it is closed off, so the setup will not look as top heavy as it currently does. A flexible wall mount would be ideal in this location, but I have already seen that this may be out of the question, because you are renting.
Personally, I would like to see the couch against the empty back wall, if you can make it fit. The polkadot chair can go against the kitchen half wall. Unfortunately, we can't see the wall that the white cabinet sits against, but if you think you can make it work, you could put the TV there with some type of stand. White cabinet will need to be moved to another place. Your other option would be to put the TV where the polka dot chair sits now. You could try to put it on a regular stand or inside a stand that encases the TV. This way you could create a sort of separation from the front door, another half wall if your will. However, it will likely box the room in and make it seem smaller, so you will have to take that into account when deciding on a stand here. TV stand options that are not as bulky may work better in this spot, such as an TV easel ora TV tension pole.
You could als try to move the couch in front of the radiator. Of course you will need to move it 8 inches or so away from the radiator to allow the flow of warm air from it. You can put a long credenza against the kitchen half wall, that covers the width of it. The TV can be put anywhere on that, the corner is probly best. It will likely come up above the half wall, so keep that in mind. The crendenza can be used for storage and further decoration on top. Another options for a stand here is a TV lift stand, so you can slide the TV in and out of it. This is expensive though. This could also be a spot where you might try a stand where the TV is encased. However this will go above the half wall as well and will likely look bulky and too large for the room