Ilya Somin at Volokh Conspiracy quotes Reagan’s 1989 Farewell Address:

I’ve spoken of the shining city all my political life, but I don’t know if I ever quite communicated what I saw when I said it. But in my mind it was a tall, proud city built on rocks stronger than oceans, wind-swept, God-blessed, and teeming with people of all kinds living in harmony and peace; a city with free ports that hummed with commerce and creativity. And if there had to be city walls, the walls had doors and the doors were open to anyone with the will and the heart to get here. (emphasis added)

and concludes himself:

Reagan’s positive attitude towards immigration was not just an isolated issue position, but was integrally linked to his generally optimistic and open vision of America. I would add that it also drew on his understanding that America is not a zero-sum game between immigrants and natives – just as he also recognized that it is not a zero-sum game between the rich and the poor. Immigration could promote prosperity and advancement for both groups in much the same way that free trade benefits both Americans and foreigners. Reagan probably did not have a detailed understanding of the economics of comparative advantage which underpins this conclusion. But he surely understood it intuitively. Those who reject Reagan’s position on immigration must, if they are to be consistent, also reject much of the rest of his approach to economic and social policy. Today’s conservatives can argue for immigration restrictions if they so choose. But they should not claim the mantle of Reagan in doing so.