I agree with dot that this is in some ways not really a question anarchists can answer without getting into the world of imagining if we had state power (and thus were not anarchists...), I do however find this question to be a timely way to explore some basic ideas I think are important to suss out about anarchism/anarchists (especially for a 101 site).
As an anarchist, I view borders and nations as arbitrary and artificially created concepts that have been imposed upon people and places as a means of control and exploitation. I oppose them, and I oppose state implemented means of restricting the migration patterns of various beings. this includes refugees from Syria, Libya and Iraq being prevented from crossing borders, this also includes salmon being prevented from returning to their spawning grounds by dams, or highways that have cut across the grazing paths of dear, the hunting grounds of wolves, etc.
I also recognize that it would be somewhat ridiculous for a white person in North America (whose family came from Scandinavia/the Baltics, the British Isles, and probably other parts of Western Europe) to wax anti-immigrant. Further, it is sort of silly for me to pretend that I have any sense of what should be done in a place I've never lived and only briefly visited (Europe).
I do think that there are things anarchists can do to show solidarity with immigrants and refugees, especially considering the current climate of protectionism, racism and proto-fascism which we find ourselves in. dot mentioned the work Greek anarchists have done in solidarity with migrant communities (comrades in Greece have a history of showing strong solidarity for migrant communities going back at least a few years to when there were racist attacks on Bulgarian migrants).
In France anarchists (among others) helped to fight against the forced eviction of the massive migrant encampment outside Calais. On the other side of the chunnel, a large and violent anti-fa showing (which most likely included at least some anarchists) confronted the National Front and the cops in a violent street fight.
Here in the Pacific Northwest U.S. anarchists have worked with undocumented people in their struggles against Immigration & Customs Enforcement (ICE), including providing support to the families of detainees at ICE facilities awaiting deportation hearings, and staging noise demos outside these facilities to let the folks inside know that there are people who care about them and that they are not forgotten.
As far as the part of the question about "poorly-kept communities" versus "higher quality communities," I expect any anarchist worth their salt is going to have problems with the idea that we should keep people out of certain areas. This sort of NIMBYism often boils down to racism, and when it doesn't, it is probably classism. In the city I live in, there are some well-to-do neighborhoods that are having this very discussion, but not about migrants (not specifically), but about homeless individuals. They fear the crime, the drugs and the squalor that they imagine goes along with increased numbers of homeless, and in at least two parts of town communities are banding together to hire private security on top of the police. We see increased security cameras and surveillance, sweeps of areas where homeless people live (the idea that because one doesn't pay rent or have a brick and mortar home that they don't have any home is also a problem, but not one I'm delving into here). To this, I don't know what to do. I think about it, I talk about it, but I have no answers.
Some other folks do projects like Food Not Bombs and Homes Not Jails to try to address these things, those sorts of direct action activist projects sometimes help in dealing with immediate needs, but it doesn't change the attitudes of people who believe they are somehow better than people with less material wealth, people from other places, who speak or look different. Then again, neither does throwing bricks at fascists (btw, either can be fun, and just because it doesn't address systemic stuff doesn't mean it isn't worthwhile).