A fiddle leaf fig is lovely and all, but it doesn't exactly give off rambling greenhouse vibes. (Sorry, buddy.) If you want your apartment to feel outdoorsy—even if it's smack in the middle of a big city—the plant you should be considering is one you've probably never even thought of: an indoor climbing vine. You know the look. Leggy tendrils reaching towards the window, leaves tapering off to tiny new sprouts near the ends. Blink and you're basically in Positano. It's enough to make a grown woman cry, seeing that frilly green growth arching so delightfully over a window frame!
Bonus: Growing one is hardly rocket science. First pick your plant depending on where you want to put it. For a low-light situation—say, atop a bookshelf in the less-bright corner of your living room—consider a Pothos, which can grow happily in all kinds of light, and let it trail down the side of the shelves. Or, if you're into the idea of window arches, pick up an Ivy or Jasmine, both of which will go totally nuts in that bright light situation. It's helpful to have some sort of feature for the plant to be trained along, whether that's a pipe or a beam or the exposed rafters along your ceiling, but not required. Most will sticky themselves right to the wall! You can just very discreet tacks to guide or "train" the vine in any direction you want it to grow, though they'll naturally creep towards the natural light source.
Other good vines to consider include Philodendrons, Arrowheads, even Black Eyed Susans for a little pop of color. Look for them in hanging baskets at the nursery, or ask what climbing vines they have in stock that might work in an indoor situation.
Let it be known, however, that this is not a no-maintenance situation. If your climber is really growing rapidly, you'll need to have the guts to clip it back on occasion (this not only keeps it from spreading in the wrong direction but also encourages a thicker, leafier result). Prune more aggressively come spring, and again in the fall if you've got a real spreader. And in general, err on the side of *under-*watering, tapering off even more in low-light of winter. Vines are pretty rigorous, however—should you totally neglect your climbing plant it might still stretch out in all directions with that slightly haphazard, highly charming legginess. Your apartment totally woke up like this!