Full of hope and excitement about something, in a way the speaker thinks is naive — you are so dazzled that you cannot see the boring or difficult parts. The picture behind it is someone whose eyes are shining, as if there were stars in them. Two typical uses: about young people beginning something (a starry-eyed graduate arriving in the big city, a starry-eyed new teacher), and about people in love (a starry-eyed couple who have known each other three weeks). It is nearly always mildly critical, but the criticism is gentle and often affectionate — the speaker usually likes the person and is a bit sad that reality will get to them. It is not the word for genuine, well-founded optimism; if the hope is sensible, you say 'hopeful' or 'optimistic'. It can also describe the hopes themselves ('starry-eyed plans'), meaning the plans ignore the real costs. It sits at the informal-to-neutral level and appears a lot in journalism.