How to improve the acoustics in my living room?
The quality of speakers in your TV are quite limited because flat-screen TV's don't have enough room for proper speaker cabinets. As other answers suggest, the already reduced-quality sound is bouncing off the wall, which further reduces the quality by creating an echo.

Definitely invest in some forward-facing speakers at a minimum. You may not have the room for a surround system, but strongly consider a center channel speaker because dialog will be more easily understood. Many companies sell kits that include an amplifier and speakers, up to and including surround systems. You can find very good quality in a relatively small size, so you shouldn't need to spend more than a couple hundred dollars at the most.

Next, the hard surface floor is going to reflect sound much more than a carpet or rug. Given that you're renting, you should probably get an area rug to cover the majority of the floor.

After solving these two problems, if you continue to dislike the sound quality, you should try to cancel echo from the walls. Since you don't want to hang anything directly on the wall, you might want to try the folding screens idea as suggested in a comment. Some fabric such as drapes can be a great help in softening the acoustic profile of the room, so you might want to additionally add drapes or fabric to decorate but also cancel some echo.

Finally, if your furniture has hard surfaces and is at right angles to the room, try turning things a bit so that there are fewer parallel surfaces. It could help to scatter the sound a bit and provide a slightly different acoustic profile.

But definitely fix the speakers first.