What a hard question! Simply, she is looking AT the 'potential home of the Obama presidential library'. The phrase 'to look out onto' is different in two ways. Firstly, it is poetic, especially in this example. Imagine someone on top of a mountain, looking 'out onto' the scene below him; it is emotional. Secondly, it probably means she is inside, looking out of a window. Regarding the '... what she hopes' part, it is more: <<Mary Case's office looks out onto the potential home of the Obama Presidential Library, which she hopes is the future of her institution.>> So, she hopes that the new library is the future of her institution. I hope this helps.