Shop carefully for a pieces you love that slide perfectly into the areas (be sure to measure carefully) or have them built. Think out side the box a long dresser or buffet could be perfect for the tv. Paint can be applied to help the pieces blend in or stand out. If you have to settle for a smaller piece for the tv fill in the side with plants to visually fill it but I would really search for a book case or another item to place in the tall area on the side. Or maybe use it for a desk if you need the office space. Don't rush the perfect pieces will come :). Make them a feature and not something ugly. P.S. You can always hang fabric (much like a curtain) in the back of the built ins to add color. Ikea has some awesome panels if you are close to one.

It looks like a nice space, despite the built-ins being a difficulty.

Whoever built the house probably designed the space where the TV is located, for an entertainment center. If that's true, you may be able to find one that will fit there, and look pretty nice.

I would look at IKEA. (I'm sure that would be your first thought, too!) They have modular pieces that I've seen used that look like built ins, and would probably be the cheapest solution, especially if it could be reconfigured if you move, or is something you like well enough to invest in.

The space on the left is rather difficult, with the restricitions of renting. Do you think the landlord would let you install a louvered door? If not , you could look for a cheap, or nice, bookcase, or cabinet with doors that fit as tightly as possible. If you like the idea of a entertainment center, and it has a wood finish, if you could find the same wood for the other area, it would tie the room together. I would try to concentrate on spending money on what you can take with you and resuse.

I wonder if a kitchen island on wheels, or a bar would fit in there. Some of the kitchen islands that are on wheels are really cool, and you could use that just about anywhere you go, or a nice cabinet. Then you could put a mirror, or a print above it, and maybe something on the walls on either side. That would look nice, and be useful. I bought one to put in a small bathroom that needed counter space. It was white wood with a granite top, which made it nice for the bathroom. Also, maybe an armiore would work.

The last thing you could consider is, installing a pull-down shade. You could use rattan, fabric, etc. Smith Noble is an online window covering company, also, Blinds Galore. Check out the websites, and even call and talk to a customer service person. I've used Blinds Galore, and they've been pretty helpful. They may have had people with the same challenges. If there is a window, you could maybe put a matching one there.

Those are the least "invasive" solutions I can think of. Good Luck! Fun challenge!

P.S.

If there is an electrical outlet, you could put a lamp on top of a cabinet, and would be really nice in front of a mirror.

If not, I've purchased really cheap battery operated, "stick-on" lights.
You maybe could stick them on something you could then tack up with a very small tack. I am editing my comment, and I see someone suggested similar things while I was writing!

Nancy's mock-up is wonderful showing what a single bookcase and larger tv/under-cabinet can do. And I love Amanda's idea to put a desk in the alcove to the left, or the next one to use it for a bar cart or console. Actually, the suggestions above make the alcoves seem like an archtectural feature that adds more interest than four square walls. Enjoy!

It does look great! I always have to remind myself to keep scale in mind, and force myself to buy bigger items.

How about a vent-less or electric fireplace with the TV mounded above it. Can you paint? if not buy some 1/4" plywood cut it the size or the wall and cover it with fabric or wallpaper to add some WOW. Good luck