Every tourist must visit Montmartre when in Paris and also must visit Hardware Societe when in Montmartre. They make the best eggs and they also have dishes for vegetarians. I definetly recommend "Baked eggs 2" which has chorizo, tomato, cheese, potato & aioli inside. And for vegetarians I recommend the mushroom one. Beside that, their homemade ice tea is insane. I would love to take a gallon but they only sell it by glass.
And for desert even though I am not a fan of cheesecake, their cheesecake is at its best! If it's possible take a seat near window & enjoy roofs of Parisian apartments. Their decoration is also pretty nice! The only problem is it's too crowded on weekend so I suggest to go there at weekdays. And also they are closed on Tuesday & Wednesday. For me the best day for going there is Monday.
Photos taken with Samsung Galaxy Note II.