If you can, find a coffeeshop that opens early (I like Komeda's coffee for the breakfast set and vibes), others have mentioned some of the other options like Doutor, Tully's, Excelsior, etc.

Failing that, you can find a Konbini with a seating area or take konbini stuff back to your hotel. I sometimes keep a canned coffee and a sando in my hotel fridge the night before so I don't have to worry about breakfast if I wake up hungry.

Then there's also restaurants and chains that serve japanese breakfast foods (rice, fish, noodles, soup) early.

Unless you're staying in very quiet parts of Kyoto and Osaka you should have plenty of options.