Honolulu is my port of entry. Went outside to explore the island overnight. Now I need go to the mainland (san francisco) which I have the ticket and boarding pass already.
Do I need to go again to immgration since it’s going to mainland?
Hawaii has been a state of the United States since August 21, 1959. I am not well versed enough in the laws of the era to know whether you needed a passport before but for sure you didn't since that, now almost sixty years. Official source has this to say:
Hawaii is a U.S. state and therefore passport documentation requirements for U.S. citizens and LPR's do not apply.
You will need some TSA approved identification and REAL ID will change the list next year, nonetheless the statement will be true: a TSA approved id is both necessary and enough to fly within the United States.