You can contact the office of Massachusetts Governor Charlie Baker at 617-725-4005. An aide will answer the phone and offer to give Governor Baker your message. Please note that you can also write or send an e-mail via the Governor's Office public contact info here, but a phone call is more immediate and likely to be noticed.
From my comment to sovay immediately afterwards:
"What felt like hours of ringing, but what was actually a couple of minutes or less, gave way finally to a polite male aide. I requested to speak to the Governor, because why not, and was told as I had expected that he was not available but that the aide would transmit a message to him on my behalf. I told him that I urged the Governor very strongly to make a stand and offer refuge to Americans threatened by the policies of the oncoming administration. I diverged from my notes a bit, so I'm not sure of my choice of words, but I remember I said that Governor Baker not only had to take a stand against bigotry and intolerance, but that he had to be seen, publicly, to do so. I may have said that we the people of Massachusetts have to set an example for the rest of the country, and that example must be to stand against intolerance and deportation, and that I was sure the Governor had often thought of John Winthrop's statement* that the eyes of the world would be upon us, and that they're upon us NOW, and we have to visibly take a stance now that the world will see us, and that stance must be against intolerance. I was angry, I got emotional, my voice shook, and to my surprise I teared up, but I hope it lent force to my statement rather than making me inaudible.
"I didn't say half of what I'd meant to say. The aide seized the first chance he had to shut me down in a genteel fashion and end the conversation. I did manage to wrap up by saying that I was a lifelong citizen of Massachusetts, a taxpayer and a voter, and that I would be awaiting Governor Baker's official reaction with great eagerness.
"This concludes today's episode of Adrenaline Theater."
*John Winthrop came out with that beautiful Christian reference about our being a city on a hill and all eyes being upon us, and proceeded to set an example to the rest of the world by persecuting religious dissenters like Anne Hutchinson, gloating over the miscarriages suffered by Hutchinson and Mary Dyer, attempting to wipe out the Pequot Indians, playing one Native American people against another, and encouraging the slave trade. What I was trying to say was that we need to visibly do better than him and his peeps.
EDIT: Since I was all geared up to use the phone anyway, I phoned Speaker of the House Paul Ryan, and left a message on his answering machine urging him to condemn the appointment of Stephen "White Supremacist Slob" Bannon. My Senators and Representative all condemned the appointment already, but I called their offices anyway and asked their aides to thank them for me and transmit my support and approval. Information for phoning Congress and other folks is here.
OTHER EDIT: Joseph Curtatone, Mayor of Somerville, has already declared it a sanctuary city and spoken in defiance of the new threats. You can also just call his office and voice your approval and support; their staff are really nice folks.