It looks like you need a pattern in the room considering that everything but your rug is a solid color.

a blue/white stripe would be nice. One panel on each window with a tie-back or hold-back on the outside edge. Maybe something like this

I think your room looks lovely without curtains. Is there a reason why you want to add them?

For your space, I like sold color panels. You could do a small pattern that reads solid or something with lots of texture to add some interest. You want the attention in the room to go to the people area, not your walls.

I would consider hanging panels on all the windows to balance the room out. If you hang them high and wide, they won't interfere with the view.

I like it the way it is too but, for privacy, I would add fabric blinds or wooden ones.

Consider woven shades for the two windows for some texture and color relief that will mesh beautifully with your modern and transitional vibe.

I think curtains on two windows only would look odd. How about pull down cellular shades? You can keep the two pulled down for privacy, and the others up for the view. They are great windows.

The moldings are very nice so I would not suggest drapes which would hide them. If you want privacy at night, you would need lined wicker shades as you see through the blinds into the house at night. I think wide slats on wooden blinds would be prefect. For color add art work (move the mirror to another location) and patterned pillows, plants, whatever you like.

Thanks everyone for your help! I really appreciate the suggestions. I considered Roman shades for these 2 windows but I thought it may look weird in relation to the 8 other windows in the room being bare. Just need privacy on these 2. So that is why I was thinking tall curtains. Now I may be even more confused though! Haha. Keep the suggestions coming!

The other windows

Are you in SC? I am getting a strong SC vibe from your decor and your yard. I lived there for many years. We are currently in Denver. I don't miss the humidity and bugs but I really don't care for the mountain style decor.