Here's a list of most places serving breakfast in Martinez. Reports are attached.
IMO the best options are Victoria's Cafe and Copper Skillet Courtyard with the edge going to Victoria's. Peg's is also open Sunday but I didn't care for it.
If you change the search criteria to brunch it turns up J.T. La Beau's and La Tapatia.
I never did report onLa Beau's because I was so underwhelmed. I may give them another chance one of these days.
Haven't tried La Tapatia for brunch but I have had lunch there. It is ok Meixan food, not great, not bad. On Sunday they have an AYCE brunch buffet which you can take a look at to see if it appeals to you. Actually Primavera is open Sunday also and would be better Mexican food if you wanted a Mexican breakfast. Haven't tried breakfast there either, but I liked what I had for lunch.
On Sunday there is also a nice farmers market in the street with La Tapatia and Victoria.