NYC is an immigrant city, but very different than the border cities. And since you have been losing population, it would do you well to replace some of your losses.
I grew up 20 miles from New York City and while it has many immigrants, they did not all suddenly show up in the last two years. Perhaps it is closer to NYC in the 1920s. At that time immigration was a problem and it led to people like my dad's father leaving Brooklyn and moving to New Jersey. But the infrastructure in Texas does not allow for that kind of migration except maybe in Dallas and Houston.
Problem is both those cities and Austin are growing so much due to intra state migration, I don't think they can handle the current level of extremal migration on top of it.
It does feel similar to when I lived in South Florida and we had massive numbers of immigrants from Haiti which overlayed with the normal high immigration level meant the population was growing far faster than the cities could handle it.
Visit Austin, I have not seen that many cranes in one place since I visited Berlin after the wall came down.
NYC should organize your own busses go to those border towns and offer 250,000 of them a place to live in NYC? I say 250,000 because that is the proportional impact on some of the border towns and smaller cities not the absolute numbers. On the other hand a more practical idea would be NYC to take maybe 50,000 immigrants based on its population and other cites take their "fair share".
Regarding Martha's Vineyard, I have been there several times. And I moved from about an hour away 10 years ago to California. Unless things have changed, the place should have embraced these immigrants with open arms. The shortage of low wage workers to support the tourist trade means rather than 50 immigrants, they should probably take a few hundred. I really have no idea why the city couldn't put the immigrants up in some of the hotels (being it is now "off season" and work with them to find jobs?
As noted, we see the problem in our Hispanic neighborhoods. We have three rental properties where the average three-bedroom two bath unit has 10 people living in it. During Covid when they lost their jobs, we waived the rent for 60 days. We provided a $300,000 mortgage to one of our hard-working Hispanic immigrants to buy a home and get out of his neighborhood which had become infiltrated by cartels and was becoming increasing dangerous as cartels vied for control. I know I am just uncaring conservative that gives 10% of his income to charity on top of helping Hispanic immigrants buy homes (the third time in my life, I have helped buy an unrelated Hispanic a home), while at the same time helping people stay in their homes during Covid... shame on me for simply pointing out the truth of the unequal distribution that has resulted from the lack of secure borders and its impact on the border communities and the immigrants.
You seem to be confused about the problem.
The bigger issue is not "immigrant" vs "non-Immigrant", the same problem would exist if huge numbers of poor American citizens with limited job skills suddenly moved into a town.
The only difference is this problem is self-inflicted since Biden has done such a poor job on the border. Meanwhile, the receiving communities had more advanced notice than when Biden transported people at night to various airports without warning.
You might enjoy this article about why the Democratic mayor of El Paso is transporting immigrants to NYC...
The really strange thing is your mayor recently said...
“As the mayor of El Paso stated, these migrants and asylum seekers are not coming to any particular city. They’re coming to America,” Adams said Sunday.
https://nypost.com/2022/09/18/el-pasos-democratic-mayor-oscar-leeser-defends-sending-migrants-to-nyc/