I mentioned some tracks in my video. Let me make a text version of some of some tracks. Pardon my "consider everything" approach...

May be a long read.
--- Japan ---
I think you can't mention Asian courses without mentioning
Suzuka Circuit. People will say I'm overrating Suzuka, but this is my favorite course in Japan. I think Japan is key for the Asian Le Mans Series. I hear that renovations or something is being done to Suzuka to prep it for when the Japanese Grand Prix (thankfully) returns to Suzuka. I think it's one of the world's toughest and most rewarding race tracks along with the likes of Interlagos and Spa-Francorchamps.
Two other nice venues to consider would be
Fuji,
Twin Ring Motegi, and
Autopolis. If you want to go with other such venues, there are a number to consider including...
Sendai Hi-Land,
Ebisu Circuit,
Nayayama Circuit,
Sugo, and
Okayama. I was going to mention Mine Circuit, but that track has been defunct since 2006.
--- South Korea ---
They may try
Everland Speedway, but the real boost will be when
the new F1 course in South Korea is complete.
--- China ---
Shanghai International Circuit and perhaps
Zhuhai would be frontrunners.
Goldenport would be a great consideration as well.
--- The Philippines ---
Only worthy circuit would be the
Batangas Racing Circuit. To me, this track is like the Philippines' version of Brasilia. Batangas Racing Circuit is more like a tangled mess of roads, but a great challenge.
Subic Bay would also be possible.
--- Singapore ---
They COULD try their own night race around the
Marina Bay Circuit in lively and lovely Singapore, but it's not very likely unless a deal can be arranged.
--- Malaysia ---
Sepang, Sepang, Sepang. Can't go wrong. A possibility would be Johor (or whatever it's known as nowadays).
--- Thailand ---
If some money and interest were put towards racing in Thailand, it would great to see the Asian Le Mans Series try out
Bira International Circuit and
Thailand Circuit.
--- Indonesia ---
Only permanent course in Indonesia is
Sentul. Wouldn't be bad to look into.
--- India ---
I am still uncertain as to any progress to make an F1 course to be held around Delhi for an Indian Grand Prix in a few years. The
Irungattukottai Circuit (or Madras Motor Sports Club) track would be a great track to maybe look into renovating to grand prix-type standards. But really, that possible F1 course in India (around Delhi or New Delhi) would be any real hope of Asian Le Mans Series action in India.
--- Middle East (Turkey, Bahrain, Qatar, and United Arab Emirates) ---
My favorite Middle Eastern course is the
Bahrain International Circuit. It's on the Asian continent, so why not an A(sian)LMS race around this exciting course?
Istanbul Park is also a can't miss course. It's just so fun to race and challenging.
Losail International Circuit in Qatar would be good to see racing around too. The
Dubai Autodrome would be interesting for a venue for this series, but I'd be interested how the
Yas Island Circuit shapes up for the 2009 season-ending F1 race.
--- Australasia ---
There are no known race tracks in Papua New Guinea, so I'll move on to Australia and New Zealand. There are a great deal of courses in Australia. I'd nominate Bathurst, but I think that would be a bit too much for the Asian LMS. So tracks like
Eastern Creek,
Sandown, and
Surfer's Paradise would be great. Don't forget about
Adelaide (street course).
Now for some Kiwi love! Really, the
Taupo Raceway would be the best bid. On the south island,
Teretonga would be nice as well.
So that's my approach- it's the ASIAN Le Mans Series, so find as many Asian circuits as you can find, and then maybe venture into some other non-continental markets for a round or two. That's an ultimate wishlist. Also nonwithstanding would be any temporary street circuits or race tracks in city parks in certain cities (like the new V8 Supercar course in Townsville). I bid you farewell.