I'd go for equaling the space that's above it, below it.

Under the Sill. I would not cut off the current window apron leave the two units as two different pieces ie the bookshelf and the Window....

I see two really attractive options for this space.
1. Build the bookshelves across the entire wall, but coming just under the sill (as others have suggested) so that they look almost like tall wainscoting.
2. Build two floor to ceiling bookshelves with crown molding on top and either a low shelf or a bench between them with cushions under the window. Ordinarily you would choose this second one with a full sized window, making a real window seat, but it could be an option here too.

Thank you for all of these ideas!

Sunterra - are you saying do the bookcase level with the bottom of the apron? Or just below the apron?

I love Feeny's idea of two tall bookcases with a bench / shelf in between. I'm thinking it could even be a type of buffet? Or space for a TV in case future owners would want to use this space as the living - which it's kind of set up for. We're not moving...just thinking ahead.

Would it be weird to have tall bookcases facing you as you come up the stairs to the house? This is a 2nd floor apartment.

Not weird in the least. People put bookcases in all sorts of unexpected places, and they look great. (Can you tell I'm a fan of bookshelves?)

I'm a big fan of bookshelves, too. Thanks, Feeny for some more great photos.