Most places will require a credit card.
As far as I know there are no places to go to buy import games and get a good deal. Your best bet is definitely ebay. I bought a second hand American PS2 for US$85 and a SNES for US$25, along with HEAPS of GBA games for less than half of what I'd have paid here - plus some of those aren't even sold here. For example, I bought all three GBA Castlevanias for US$25 from America. In Australia only one has been released and you could expect to pay $25 for a second hand copy for that one game alone. I also bought Chrono Cross, an excellent game that you can buy extremely cheap on ebay atm, which has never been released here.
The only problem you may run into is if you buy a console, you may need a transformer. These are big things that convert the voltage from Australian voltage to American, and are generally outrageously expensive - I got mine for $99. You will also need a TV that can run the TV signal - if you buy an American console you will need a TV that can run NTSC signals.
If you want just portable games, then don't worry as all Nintendo handheld games are region free (capable of running on a handheld model from any country). PSP games are mostly region-free, but a select few aren't.
ONE MORE THING and this is important. If you buy games on ebay watch out for piraters who may be selling bootlegs. These aren't quality assured and you may have troubles running these illegal game copies. Generally I've not found this to be a problem when buying PS2 or SNES games, but it is a BIG problem with Nintendo handheld games. DO NOT buy anything from Thailand or China. They are pirates 99% of the time. Of course, you have to use your common sense. If someone is selling 'Pokemon SHINYGOLD version' then you'd have to be daft to buy it. (There is no such thing as a SHINYGOLD version of Pokemon).