I would install rods and hang curtains outside of the alcove on the wall. It might be fun to paint the inside of the alcove a bit darker than the wall color.

That's a good idea! Now just trying to find the right kind of curtains is the hard part :/

Do you want a solid or a print? If your couch is solid, it might be fun to go with a print.

Yes I would like a print curtain. I have a few cheetah decor . Is it ok to mix match patterns for example, cheetah with chevron or trellis decor?

Those patterns would work well together. Pick up the brown/gold color from the cheetah print in the pattern, i.e., you could choose a brown or gold and off white chevron print. (See photo). After choosing curtains you could add an accessorizing color to bring in more interest.