Can Former Mayor Giuliani run for Mayor again If so is there a waiting time?

Well he's pretty much settled in with his business right now so he probably wouldn't run - but he would be eligible because current Mayor Michael Bloomberg approved the new law allowing 3 consecutive (unlimited total just no more than 3 in a row) terms for mayor and city council members. So yes he can just he would have to leave his business which he probably won't do. The wait after 3 consecutive terms is 1 term (each term = 4 years)