Since there’s hardly anything in Dubai that is walking distance from anywhere, I would suggest you stay somewhere close to the Trade Center area. It’s not as congested as Bur Dubai and Deira, but is not too far away from it either.
DUBAI INTERNATIONAL HOTEL APARTMENTS looks good location-wise, but of course I don’t know whether it’s any good as a place to stay. Maybe someone else who has stayed there can shed some light on it
Since you’ve never been to Dubai before and never driven on the roads here, I would advise you NOT to rent a car. You’ll be much better off with taxis. They are much cheaper than in Europe and you won’t get lost on the confusing roads of Dubai. The Dubai Metro is currently more a tourist attraction than a real means of transport, as it only covers a limited number of areas in Dubai.
I’ve always booked my Desert Safaris with FSN Travel & Tour L.L.C. On one occasion they were a bit late in picking us up. But other than that it has been a nice experience every time. And they are reasonably priced as well.
I’ve never been to the one in Atlantis, but Wild Wadi is definitely a nice place to go to.