Dive Centres in Dubai are very limited.
Dubai is wrecks only and the vis can be variable. The sea can be a bit choppy and sometimes there are some currents which put people off
The only centre likely to dive off the Dubai coast are Scuba shade based in the Habtoor Grand Hotel near Dubai Marina. I've never dived with them but I do know their staff and they're okay people.
The Dive Clubs in Abu Dhabi, Sharjah and Dubai (BSAC) do dive off the Dubai coast, but their diving is sporadic
The East Coast (Fujeriah) is 100 miles away and a 2hr drive. Diving is reef and small wrecks. The Vis can be variable too as is the temps depending on currents and Thermocline's (currently 28C on teh surface, chance of 23/24C below 18m
There is (as pointed out above) Barracuda based in the Fujeriah Marine club. They have two or 3 sites close by but other sites need a 40 minute + boat ride
Further along teh Coast there are a number of Dive Centres, Sandy Beach, Freestyle and Divers Down. All good centres, but you'll need yoru own transport to get there
Al Boom have a Centre in Dubai (pool) and Fujeriah. They do operate a mini bus from Dubai. They are a busy centre and their boats have a lot of inexperienced / occasional divers onboard. Not everyone's choice