The phrase "hopeful eyes" refers to the expression in someone's eyes when they are optimistic and believe that something good may happen. Full definition
50 plus dating gives you new way to explore life and see the beauty of world with hopeful eyes. (50plusdatingsite.com)
An aired out clean smelling room puts interested parties in the right mood, leaving them free to see the house with hopeful eyes. (hrstagingdesign.com)
Instead, he turned a somewhat hopeful eye toward 2016, when many anticipate the Democrats will ride elevated voter turnout in the presidential election and take the majority in the State Senate. (observer.com)