If you choose SE Asia you need to be aware of several things.

1. Health. If you're going to cycle in rural areas such as the Mekong delta of the parks of Thailand consider rabies shots. Dogs are everywhere and they tend to steer clear of humans, but rabies is endemic and frequently, at least in Thailand, rabies regions are declared. You'll also need Hepatitis A and Typhoid, though I'm not convinced by the latter. These are the Air France recommendations, by the way.
2. Medical insurance. Be aware that both health and care can be primitive, certainly in Cambodia and parts of Vietnam, so health insurance that covers evacuation you to a Thai hospital is a good idea, Thailand has the best facilities in the region, outside of Singapore and Malaysia.
3. Camping. As someone said, forget the camping gear, you won't need it. Hotels and hostels can be had for very little in all three countries, plus food if you're willing to eat off the street (I do)
4. Water. Buy it, don't drink tap water, and don't wash your teeth in tap water either. Make sure your bikes have 2 bottles each, and fill wherever you can.
5. Clothes. If you can find a locker at the airport or a hotel dump your winter clothes there, you won't need them. Wear high visibility T shirts - see 11 below.
6. Heat. Travel in the early hours, and stop early. I'm having to do a 100km leg in Cambodia early next year. Thankfully there are buses on my route and I'll be taking a folding bike, which trains, taxis and buses usually take without a problem. How many would accept a touring bike, I don't know.
7. Planning. You need good maps, and, if you're using a smartphone, download the maps you need before you go. Companies like Komoot have extensive maps, though areas like Tonle Sap don't have much more than the main road marked.
8. Language. In rural areas no-one speaks English, and even in the major cities you won't find many outside the tourist industry.
9. Smartphone. Assuming you have one, buy a SIM on arrival - you can do so easily at the airports in Thailand, and there readily available HCM. You'll find them easily in Phnom Penh too, but, if you choose to go over a land border, they're not so easy to find. The big advantage is the prices are cheap, local calls are often free, and you can use the in-built GPS for next to nothing. Well worth the effort.
10. Food. Eat in the busiest places you can find. Street food has a fast turnover and is usually fine, especially in the popular places like Yaowarat Road in Bangkok. Similarly, the tourist restaurants in Siem Reap are fine.
11. Traffic. It's your choice, but Thailand has an unenviable reputation for accidents on the major highways. Smaller roads are fine, and you'll now find bike paths in some areas, including, paradoxically, Suvarnabhumi Airport. For the major cities, especially in Vietnam, motos are a real menace.
12. Tourist havens such as Pattaya (don't go) or some of the islands have every rip-off imaginable, so be wary both of friendly locals and tourists offering great deals, to help you out etc etc.

My picks? Siem Reap, because everyone should visit one of the great sites on the planet, Angkor, plus the Cambodians are lovely people, and the roads are quiet so cycling between the sites is easy. Big selection of accommodation. Second would be Hoi An in Vietnam - again, good infrastructure, plus you can visit the thriving city of Da Nang then continue to Huế on a spectacular railway trip that crosses a range of hills/montains on the coast. Third choice would be Hua Hin and south to Bang Saphan, which takes you through some National Parks and lovely coastal areas. There's a bus that connects Hua Hin directly to Suvarnabhumi, so getting there is a breeze, and you can sleep off some of the jetlag on the way.

One final thing: do check with your Foreign Affairs department for travel warnings before you leave. Border areas in particular can be hot spots.