Best Living Area in Dubai

Don't understand your question.  Best area for living could mean different things to different people.   

It could be the most luxurious e.g. Emirates Hills has big mansion type houses with rentals ranging from AED 600K to 1 mn a year.  Palm Jumeriah has villas for 300K+ a year.

Or it could be best areas within a budget.  You need to be clear with your question.

jumeirah lakes tower is good environmentally and economy vise. marina and palm jumeirah is good too

Jbr is the best

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It depends on your budget and the place of occupation.
Either you can plan to rent an apartment/villa in the far neighbourhoods where the rent is low. Technically, you can travel everywhere in a car, but practically the traffic is a hassle in Dubai.
Or you can get a place near your office. Transit becomes easy. Like a friend of mine working in Dubai Production City, rented out in the nearest neighbourhood, Jumeirah Village Circle. He has access to all the amenities including a small shopping mall. We hang out there some time. Travelling to office is so easy for him and that is not the case for most expats.
So, calculate your budget with comfort to decide the best place for your to stay in Dubai.

If you are looking for some cheap rents then you should try in international city Dubai