When to look, if want apartment available Aug 1?

Daughter moving to NYC at end of July. Hoping to find 1 Bedroom apartment that will be available for a 1 Aug move-in. Any advice as to when we should look? Also, would appreciate advice on whether or not $1500 will get her a 1 Bedroom in a safe neighborhood. She’ll be working in lower Manhattan but are thinking Manhattan is probably too expensive for her budget, so are leaning toward Brooklyn. Any thoughts would be greatly appreciated.