I'm in my 8th month and seeing Dr. Agatha Moniz from Medcare Women and Children hospital along Sheikh Zayed road. She came highly recommended by friends. I had switched from another gyne who had recommended her in case of emergencies. I love her. She is patient and and gives you time and attends to all your queries. The hospital has a reasonable maternity package.
I also heard American hospital is good and Zahra hospital as well. You can check these.
Take care!
I think American Hospital is a good choice - I'm currently seeing Dr Raj and she's great, and I have friends who have delivered with both Dr Raj and Dr Braithwaite and I've heard only good things.
American Hospital is also the costliest, so as long as your insurance covers it you'll be fine.
Good luck!