Landbased or boat/kayak?
Great options from a boat or kayak 15 mins away up at Leigh. Have not done much from the shore though. I normally fish out of Leigh harbour and head over to Leigh reef, the outpost or Daniels reef. Normally schools of kahawai working Leigh reef and surrounding area this time of year. Should also be in Omaha bay. Just look for birds. Could be kings around with the schools.
Shallow weedy areas around the coastline produce snapper on the drift with a fly.Most of the area can be reached easily with a kayak, even Leigh reef. Just don't go into the Marine reserve around the corner at Goat Island.
Have not fished Omaha a great deal other than taking my son to catch sprats off Ti Point wharf, but that is too packed to fly fish most of the time. If you are shore based I would look for some access to weedy rocky shorelines. A bit of berley (if you are that way inclined) and they should produce well. Have tried the channel that runs out of the estuary (accessed from Point Wells) but have not caught a thing even though it looks great and I know the channel holds trevally.