I found this cool place where you can stay in 'capsules' for like 4,000 Yen a night right near tokyo... so I think its a mos def.
Most capsule hotels don't allow foreigners to stay for long periods. Anyway there isn't a reservation system with them, everyone packs up before midday, then at a certain time they re-open just in time for the salarymen to miss their trains and need a bed for the night. I used one after a big night in Shibuya, being 6ft 4, shit was mad claustrophobic - can't recommend it at all.
If you do Tokyo, you're gonna need a LOT of time there to really explore the city; not to mention a fair bit of cash. Very average hotels are around the $1K USD for 7 nights, basic small room with nothing extra.
Out of your list, I would skip Singapore, instead focus more on Tokyo + HK (with a trip to Macau).