Going to NYC for honeymoon WTF to do?

My fiancé is from the Bronx and she loves NY and her dad is gonna pay for travel and room we just gotta cover whatever we do while there so it's not exactly a bad deal.

The 2 of us have traveled all over the US and Europe probably at least 35 countries each of us have visited. So we don't care about going to typical spots like Italy, or Spain, etc.

Anyways I'm from CA and have never gone to NY let alone NYC. WTF are we gonna do for a week in that city without breaking the bank. Because when I think of NYC I think of Los Angeles but dreary and more expensive without the beach.