I'm sure there's somewhere in Carmel, but the best Mexican will be in Seaside. Last time I was there, the taco shop in the back of Mi Tierra Mkt at the corner of Broadway and Fremont was excellent, and you could get stuff to go and drive down to the beach where there's parking.
re: Ed Dibble
I think most of us can agree that sit-down Mexican dining, except in very large metro areas, is pretty sucky in California. It's all bland moles, canned chiles and gobs of orange cheese. The real flavor and ingredients are to be found in the take-out deli counters and from the food trucks servicing Hispanic neighborhoods and ag field operations.
Melanie Wong and other Bay Area hounds have detailed Mexican food trucks in Salinas, about 15 minutes inland--the choices are staggering. At the coast, the business districts catering to Hispanic shoppers are in Seaside and Marina. Most all grocery stores, from large markets to small bodegas, have a hot deli counter with various dishes to go. Some even have a few cursory tables or chairs for quick on-the-spot chowing. I second Ed's rec to grab some favorite items to go, and don't travel too far to enjoy them. There is plenty of gorgeous scenery nearby.
If you are in the mood for a good coffee and delicious Euro pastries, I want to rec Sweet Elena's nearby in Sand City near Highway 1 just west of Seaside. It's a bit hard to find but google and you'll see. It's in a funky ancient industrial area, and it rocks. Traditional French pastries and wonderful coffee drinks, locals' artwork on the walls.
here's a link to pet friendly dining in Monterey. Looks like a spot where establishments can advertise, so I'd take the comments with a grain of salt, though I do like Cafe Fina on the Wharf.