The places OP mentioned, Shibuya, Tsukiji, Sensoji, LaQua, and Oedo, are all in different neighborhoods. I would focus on one area at a time so you spend less time traveling and more time shopping.

Another cheap place to snooze are manga cafes. There are sure to be many near each train station for those who missed the last train and don't want to take the taxi home. They often have a shower but nowhere as nice as the spas.

I have done something similar in the past. Went to Akihabara and bounced between stores until I got tired at 2 AM. Checked into a manga cafe using their 5 hours for 1500 yen special. Also took a shower that cost 400 yen. Caught the 7AM discount bus to NRT the next morning.