Obama's father and his people came from a village in western Kenya, not far from Lake Victoria. Mombassa is a seaport on the eastern shore hundreds of miles away. Why would she go to a hospital there instead of, say, Nairobi which is closer and was also the colonial capitol?
Why did Obama's father decide to go to school in Hawaii and later in MA at Harvard? Why did cousin Odinga go to Communist East Germany for his education?
Just because Wikipedia says Obama's father and tribe mostly lived in western Kenya doesn't mean that none of them ever spent time anywhere else for any number of reasons.
My children were born in different hospitals that were hundreds of miles away from where I and my spouse came from.
I have no idea what took the Obamas to Mombasa. If you want to know why they were there, you should look up Grandma Sarah Obama and ask her as she is the one who said they were there. Oh wait. You can't ask her because she is being kept quiet.