It depends on where you want to go in those days. You can check out www.hotwire.com to get some decent rates (hopefully). The catch is you won't know where you're staying until after you pay. However, I've tried them out and it's never been bad. (Example was a room in the Hilton for US$40.)

If you're going to be in the Hollywood area, you might end up staying close to the Red Line of the Metro subway. That branches out to different places and they have a stop at Universal Studios Hollywood if you want to go there. There's also a line going to the airport. I think there are two transfers to get to the airport though.

It's very hard to get around without a car as public transit is not that reliable. Hope you can solve this problem though.

Good luck and enjoy your short stay!

Oddly, one of the best budget places to stay is seaside in ritzy Santa Monica, or anywhere along the line of it's bluebus network (under a dollar, connects to LAX, Getty Museum, UCLA, etc). Do a google search on bluebus, hostels, etc.

Chant,
I like downtown, but I wouldn't stay there unless you're headed to the opera or theatre. It still is fairly dead at night ( some exceptions).

The Hollywood -Sunset area is a lot more lively and near the Metro lines. The Roosevelt in Hollywood is an upscale hotel, but does run specials frequently. You might even check the new Millenium Hotel (don't know what you consider cheap...also don't know the prices of the those two). The Magic Hotel , near the Magic Castle, is inexpensive and I believe there's a BEst Western right on Highland near the Hollywood Bowl ( could be noisy).

On Sunset check the Standard and there's also a Best Western. LA has all the usual chain motels ( Days Inn, Motel 6) etc. and those would be worth a look.

The Santa Monica suggestion is a good one as you would be much nearer to the airport and the beach area can be fun.Also, you would be near the Getty if that's on your agenda.

Caution: LA without a car is difficult.

Enjoy.

I go to LA several times a year and Santa Monica is easily the best bet, you won't need a car if you stay in the area.

Try and get something near the pedestrianised area, just north of the pier

http://www.santamonica.com/

I second Santa Monica. Their bus fares are half of the MTA rate, and SM is well situated to give you best bus access to the more tourist-friendly areas of the city. Not only the Getty, etc, but good access to the Wilshire and Santa Monica boulevard strips. Not only this, but SM is one of the more pedestrian-friendly areas of LA.

Seriously, you really can't go wrong with Santa Monica, I highly recommend it for you.

There are several good choices, but rates very depending on time of year, day of the week, etc.

When are you coming, and what does an Aussie consider "fairly cheap"?

We are arriving on Thanksgiving weekend

Really, Thanksgiving weekend?! That's great! This would be a wonderful opportunity to experience a bit of American culture. Find a restaurant in the area that is serving a traditional Thanksgiving meal and make a reservation. It is classic American fare: slices of roasted turkey and the tasty bread stuffing, mashed potatoes and gravy, cranberry jelly, sweet glazed carrots, and green beans in mushroom sauce with crispy onion topping. Mmmmm.... Then, right after engorging yourself during the traditionally early-served dinner, find a nice place to relax and digest your food and catch the end of the traditional American football games that are played on that day. It is normally family time, time when far-flung relatives fly in to reunite, enjoy some great food, tip back a beer or six, watch football, and catch up with each other, and give thanks for our family and other blessings in life.

I think the major impact this is going to have on you is the airport. Because of the family nature of the Thanksgiving holiday, the airport is going to be extremely busy. This, on top of the recent security regime, and the fact that LAX is a terribly cramped facility for the volume it handles, is good reason for you to allow ample time before your flight to NYC. Allow at least two hours AT the airport, no kidding here.

Best wishes