In Japan, working in Cafes isn’t so common. However, Coworking Spaces (コワーキングスペース in Japanese) have boomed recently, and meet your requirements (except for maybe great coffee…).
I’ve listed up some co-working spaces that I think match your requirements. I’ve only been to the ones in Tokyo myself though. I’ve included the price for a day of working there, though some have an hourly rate (though it tends to be around ¥500 per hour, so if you’re working more than a couple of hours, you’ll be paying the day rate anyways).
Tokyo Coworking Spaces
co-working space kayabacho, co-edo - ¥1,000/day
Shimo-kitazawa Open Source Cafe - ¥1,000 / day
CASE Shinjuku - ¥1,920/day
Osaka Coworking Spaces
Co-labo - ¥1,000 / day
JUSO Coworking - ¥1,080/day
Hiroshima Coworking Spaces
Moving On - ¥1,388 / day
Shake Hands - ¥1,800 / day
Fukuoka Coworking spaces
Yoka-lab - ¥1,000 / day
Bases Fukuoka - ¥1,000 /day (9am - 5pm)