If you don't want to show ID at the hotel, it's probably best to remember a Japanese address and claim to be living in Japan.

I wouldn't recommend actually going there without ID. There's a small chance you'd be stopped by cops at a railway station or something and asked for ID - which means alien registration card if you're resident in Japan and passport if you're not. Failure to have ID with you could result in some wasted time at a police station.

I'm not saying that I think it's appropriate that you should be asked for ID by the police, just saying that's something that does occasionally happen. If a hotel demands ID and you refuse on the grounds that you live in Japan, you can just walk away without consequences. Not so with the police.