Be warned, HCBC is waiting like a wolf at the door for new-joiners. As a previous poster stated, they will come to your home, sign you up and then disappear. The good service ends with your signature.
Having said that, most of the banks in Dubai have shocking to non-existent service in my experience. Mashreq has been disappointing, but I have found that their online banking requires few visits to a branch, so suits me fine, coupled with 2 free international transfers a month.
I enjoy Lloyds for generally speaking being able to talk to someone who seems to know something about banking and discuss it in English without the usual Dubai comms problems.
We all have individual needs, so finding the right bank can be a real chore.