Life in Dubai is great depending on your socioeconomic status, attitude, and ability to adjust to a variety of cultures.
I have been in Dubai for almost a year now and love it. Coming from the USA, I think it is a great place to live. It is a cultural melting pot like New York. However, there are a number of things to keep in mind.
1. Socioeconomics: Dubai, like any other city, is great as long as you have a JOB that will allow you to live comfortably and prosper. Those on low wages struggle here because it can be expensive. However, there are areas of the Emirate that are less expensive to live than the high priced typical Expat communities. Most people come here already being sponsored by a company that they will work for here in the region. However, some Expats come and do have success finding a job once here. The recession has had an impact and some that come on a whim have had difficulty finding a position. Therefore, I would highly recommend having a job in hand before you come no matter your nationality.
2. Attitude: If you have a positive attitude and can adjust to change, you will do well in Dubai. You must be willing to go with the flow and not get upset over minor issues like traffic. There has been tremendous growth in the Emirate so traffic can get busy during rush hour. But, this is no different than most cities.
There will be continued construction and traffic detours that can change frequently, but that is the cost of a growing city.
3. Cultural Diversity: If you come to Dubai and are open to other cultures and people from different backgrounds, you will be fine. There are so many different nationalities here that it is totally amazing. Not all these individuals come from countries as rich as Western countries. Many come from poorer countries to work in the service industries here and send money back home to their families. You definitely see that difference between the socioeconomic backgrounds of various individuals. But, everyone is working hard to take care of their families regardless of background. I have found that Blacks do fine here and will have a different experience based on their socioeconomic status just like everone else.
If you come to Dubai and only hang out with other Expats or stay in a bubble, you will have a totally different experience than if you try to get to know local Emirati's and local culture. Some Expats try to learn Arabic, which is a plus. However, some Expats have come and lived here 10 or 15 years and never attempted to learn Arabic or get to know the local Emirati people, which is unfortunate. Although it can be difficult to find opportunities to socialize with them, but the Emirati people are wonderful.
Caution: Do obey all laws in the Emirate. This is the only thing that will get you in trouble and make life miserable. Depending on the law broken, you will promptly be deported.
4. There are variety of professional organizations for women in the Emirate including the American Business Womens Association, International Business Womens Association, an Australian Group and many other groups for networking or starting a business. There are some informal groups of Blacks that meet socially. These Blacks come from all over the world, but because they live in Dubai, they have tried to form a bond and get to know one another in social settings.
I have not seen anything "official" set up through the government or any other organization.
5. Miscellaneous:
a. There is no need to cover up here in an abaya. You can just wear normal clothes that respect local culture.
b. Black hair care products- these can be challenging to find in the Emirate. There are a few salons that offer some supplies. Some salons like Zulekha do braids and dreadlocks.
Additionally, there are celebrity lace front wigs for black women at Sheer Lace Dubai for ladies that want problem free styled human wigs like Beyonce & Tyra Banks or extensions.

Hope this was helpful!
DuGal