Rydges wins for convenience - at least presuming that you're flying international (getting to domestic requires catching the T-Bus between terminals, although if you're catching QF you can also catch their bus). However it's not the cheap option.

For Domestic, there's a few that are pretty much on the airport grounds and a short walk from the terminal (eg, Mantra and Ibis Budget) and then a grouping of them in Mascot which is in the longer-walk-or-short-taxi range. Most recently I've stayed at the Moxy which seems to be one of the few that has a shuttle to the airport. When I last stayed there the shuttle was paid for most people (although seemingly included in some corporate rates), but it looks like they've changed that and it's now free for everyone.