Can't speak about suits, but I got some good shirts made at Whistle & Flute in Satwa, in a little alley behind the Iranian hospital. They do suits as well so might be worth a try.
I only just saw this 'thread' (sorry!).
Kachins in Meena Bazaar, Bur Dubai, 04 3521386, they have from cheap materials right up to the very best Yorkshire produced yarns. Great range and very good workmanship.