Blisteringly hot in summer, Tokyo is a breeze in the cooler months. Fight the dizzying jet lag and head out for the world's best sushi or ramen, shop in the city's amazing department stores, and visit the parks surrounding the Imperial Palace in the center of the city. Escape the crowds somewhat by heading to Yanaka Ginza, which retains a bit of old Tokyo and has plenty of places to eat and shop. Do make time for a side trip to Hakone, where you can visit a Shinto shrine and see magnificent Mount Fuji on a clear day.
Southeast Asia is easier to deal with, and there are cheap flights connecting in the Middle East and landing in Bangkok, Kuala Lumpur, and Singapore. Each of those is a very interesting city, and there are many smaller places to go in the same region. In Malaysia there is Penang and Melaka. In Thailand there is Chiang Mai and quite a few others in that area. In Laos you can visit Luang Prabang, which sounds like it could be a winner for you. And there is also Siem Reap, which is home to the amazing Angkor Wat temple complex.