Bankstown has a tower and the few times I have flown in (IFR) they have been easy to deal with. The standard IFR routes work pretty smoothly from the South & West.
Bankstown is probably an easier destination for Sydney's unreliable taxi's.
Bankstown has some coffee shops / sandwich shops if you end up needing to kill some time.
Wollongong might be easier than you imagine and depending on time of day may not be much slower to get to than Bankstown. Its pretty quick driving South from Kingsford-Smith. I wouldn't dismiss it lightly. A mix of train to get out of the airport environs then Uber might go well.