I don't know about Beijing, smog capital or the world probably. You can visit the great wall, forbidden palace, and emperors' tombs. Shanghai have some interesting buildings, visit Cheng Huang Miao and maybe taguanyuan. lots of good food there, if you can stand how many people there are.
I have been to Malaysia and Singapore. Nice clean places and very friendly people. Since I live in Boston/NYC, frankly, there was not much for me to do or get excited about in Kuala Lumpur or Singapore. You can try out the bird park? They have a number of species and you can participate in bird feeding etc. Food is fantastic and also very cheap. As rocketsjudoka mentioned, try Nasi Lemak and Roti Chennai out. Also try out different variations of Asam Laska. Its a fish based soup with noodles etc. and each state has its own variations. Dont forget to order plenty of fresh coconut water. Try this restaurant in KL. We liked it. http://www.nailisplace.com/ This restaurant is pretty good... Ole Ole Bali And if you go to Malaysia, you have to have Satay. From our experience, this chain is the best... Sate Kajag Haji Samuri They serve fresh off the grill satay (chicken, beef, rabbit, deer). They are all fresh and delicious!! MUST HAVE! You will find several other very nice restaurants at Petronas Tower/Mall. I also like their fresh fruit stalls within the malls. They have different kinds of fresh fruits all sliced up and bagged for 1-2 ringgits to enjoy on the go. We loved the fresh mangoes (sweet as well as sour), papayas, guavas, dragonsfruits, etc. If you have time I would recommend going out to one of their islands (Lengkawi, Redang, Tioman). Beautiful beaches with plenty of activities for families. You can fly local planes from KLIA to one of these islands.
You only need a visa for China. I used to be able to get my China visa in Hong Kong in a day, but I don't know if that is true anymore. As long as you aren't there for business, you are good to go. There are companies that do the visa thing for you and all you have to do mail them the stuff. It's a lot cheaper than gas going down to Houston and back twice. I used CIBT.
You can still get a visa in Hong Kong for the PRC. You can do it in a day but it will be more expensive. The standard wait time in Hong Kong is only a couple of days so if you are planning on visiting Hong Kong for awhile you are probably fine with doing the standard wait. There are options for multiple entries which aren't much more expensive than the single entry visa. There is a lot to see in Beijing besides smog and definitely recommend visiting. One thing to be careful of is to get prices in advance for everything.
in beijing it's good to get a guide who speaks english. the typical tourist sites are the hutong (old town alleyways), nightmarket with insects etc, forbidden palace (make sure to visit the park behind with the hilltop views of the city), and one of the 3 main sections of the great wall (do some research on which section is best for you). shanghai is really really nice. you won't need a guide there. i prefer staying on the bund or near there (the new city across the river called pudong is too corporate and boring). try to make a daytrip to suzhou, they have several spectactual parks/gardens there in tokyo, visit ginza/shinjuku/harajuku. the city is so big that if you friends or contacts there it'll help a lot when going out to clubs/restaurants kyoto is a bit overhyped imo. there are about 3 dozen sites to see there, but nothing as spectacular as what you find in china or even thailand. i did like the inari shrine though. in HK make sure to visit the big buddha on lantau island bangkok is the most touristed city in the world. really hot and humid there always. lots of shopping malls. make sure to get a proper thai massage, you can look on tripadvisor for the best spas to visit there. i also recommend a meal at the verandah outdoor cafe overlooking the river at the mandarin oriental hotel. the morning program at the tiger temple (3hrs drive outside of bangkok) is also quite good as zboy mentioned for singapore, the bird park is interesting (although a bit of a drive). not much else to do there other than shopping on orchard road and trying out the very tasty cuisine
either stay at a ryokan in the mountains for a couple days example: http://www.theguardian.com/travel/2012/feb/03/maruhaci-ryokan-takayama-maze-japan ..or go to miyajima (near hiroshima) ...or if you like castles go to himeji near kobe (not a place of rape) btw, the people in japan on the whole are the most polite, helpful, and sincere i've ever seen
Bring plenty of condoms. For easy lays go to a pub called Hub. They're scattered around Tokyo near the stations. Shibuya and Machida are good ones. At Shibuya there are plenty of clubs. Harlem is the premier hiphop club and Womb, Ageha, and Eleven for house/techno etc. Roppongi has plenty of prostitutes and dirty clubs if you're into the pop clubs. Stay away from hostess bars and anything a Nigerian tries to take you to.
Besides the Bird Park the Singapore Zoo is really good and has a night safari that is interesting. Pro-Tip watch out for the flying squirrels in their habitat.
