I have done Christmas and NYE in KL, Singapore and Jakarta. Not sure if your comment about 'formally celebrate' is a joke or not, but Hong Kong and Malaysia both celebrate NYE and Christmas in a similar way to Australia. There is a public holiday on both days in both countries. Fireworks and count down for NYE. Of course a lot of non-christians won't celebrate Christmas as much, but they still get a holiday. All the shops still try to cash in on it.
KL - I would suggest either Sky bar or Luna bar for NYE. Two roof tops bars in KL that give a great view of the fire works, but you will have to book a table. Sky Bar has a good view of the goings on a KLCC park and the fireworks by KLCC. For Christmas all the malls in the city have Christmas decorations. Starhill Gallery (an expensive shopping mall) had a snow making machine inside, despite it being 30 degrees outside.
Singapore - there was a big free public event by Marina Bay although some of the locals don't like the number of 'foreign workers' (which means Filipino, Indian, Bangladeshi and Indonesian construction workers), but not really an issue to me. There is also a big NYE party on Sentosa, but more for the 20-35 crowd.
Jakarta - the security adviser from work advised against attending the main event in the city. So I went to a NYE event at a suburban mall with a local friend. The event was guarded by 6 soldiers with assault rifles and hand grenades. Standard NYE event a concert followed, count down and then fireworks. Choose to stay in a local hotel that night rather than battle traffic jams back into the city.