I would vote for UAE in general, Bahrain is good for bachelor's life and in my opinion does not have a business culture. Yes indeed in my experience it is good for a visit of few days to have fun and good time.

Abu Dhabi is the best place for family life as well as for business. Infrastructure, Schools and facilities are good and reasonablly priced, no traffic and communting problems, living costs comparatively are less than Dubai and Doha and of course it is a main city in Middle East with all right connections to base Middle East and African Operations. If you are too concerend about the costs there are cheaper options available too in Abu Dhabi like for instance living and operating from "Mussaffah" which is the Industrial city of Abu Dhabi or from Al Ain which is another city of Abu Dhabi and many International Companies have their offices there.

Business wise it is a good choice since Abu Dhabi's economy is booming due to a lot of projects in pipeline and expansion plans in future that provides numerous business opportunties for all businesses. There are no taxes in Abu Dhabi/UAE but on the other hand businesses in Bahrain are subject to taxation as per my information.

You can also think of another Emirate in UAE like for instance Sharjah or Ajman these Emirates are close to Dubai and cost of living wise cheaper than other major cities in Middle East.