What part of RI are you from? I used to live out there a long time ago

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In answer to your questions:
1. I think this area has much less racism than other parts of the country. I am sure it exists to some degree like all areas, but since there is a large military presence you get a mix of all types of people living together. As far as living on one income of 55K-70K I think in this area it would be very difficult to do. A lot of it depends on how you live. If you are looking to buy and use the rule of house price = 3 times your income, that would put your range from $165K to $210K, here that would probably only get you a condo/townhouse (it may buy a house in an area you definitely don't want to live).
2. I think new comers here are welcome, and I found this area much more friendly than RI (although anywhere is probably more friendly than RI

). Again, with the military being here, people are always coming and going so this area is used to new comers.
3. Not many for such a big city, but there is definitely stuff here like museums, concerts, history sites, etc. I like the historic Williamsburg area.
4. Unfortunately, $1000K per month will not get you a home, to buy or to rent. I recently checked my last one bedroom apartment in an ok community and it was renting for $900 per month. Prices are very high here. It might get you a two bedroom place somewhere, not sure how many kids you have. Maybe something bigger, but be very careful about what area you end up in especially if you are moving and do not know this area. Feel free to ask about any potential areas you find.
To your main question of is this a good place to raise a family. I know people that like it here and people that hate it here. In my opinion, it is by all means not the worst place to raise a family, but not the best place. I personally am not a big fan of this area for reasons I have mentioned on other posts. But that is just me. For someone new to this area, it does take a lot of money to live well here. My wife and I are in the same boat. We want to find a nice house in a decent area, but everything is so expensive. I would check this area out, but look at other cities south of here that are near or somewhat near the ocean. You will find the cost of living much less, especially if you want to keep being a stay at home Mom.
Good luck with whatever you decide to do and let us know if you have any more questions.