Most, but not all, of the Tokyu Stay apartment hotels (they also accept short-term guests) provide some kind of breakfast. This can range from coffee and toast at Monzen-Nakacho to toast, eggs, salad, and unlimited coffee or tea at Shibuya Shin-Minamiguchi.
The Toyoko Inns give you a disconcerting mixture of miso soup, onigiri, and coffee.
I've often gotten breakfast buffets at non-chain business hotels, but the assortment of foods may not be to Western tastes. However, there is always coffee, eggs, and some kind of bread or rolls if you can't face chikuwa in the morning.