Tokyo is a budget-buster, although staying with friends will help ease the pain. I'm sure they will show you around the obligatory sights, so the rest is up to your own interests.

Asia is a darned big place, so you can forget about seeing it all in month. Pick a few places that sound interesting and keep things flexible, there's no need to plan everything in advance.

Singapore, Kuala Lumpur and Bangkok all have excellent plane connectivity and supercheap flights on LCCs. The overnight train from Sing to KL is alright, especially if you're one of those people like me who hate sitting on buses, but it's not terribly exciting unless you like counting palm trees. From KL, fly out to Kota Bharu and head to the Perhentian Islands, one of the most beautiful places on the planet.