I would recommend a huge restaurant and go when it first opens. That way if it's a sit down place, you may tell them of your situation and ask to be sit typically away where they'd normally start seating people. Or if it's a place like, Simpsons Fast Food Blvd, you can just go when it opens and kind of sit in a corner somewhere and if too many come near you and make too much noise, you can simply move somewhere else, or leave and still be able to bring your food with you. I've eaten there first thing and it's relatively quiet, there's no loud music and where you get your food (which would be the only place to have activity when it first opens) is away from the dining area.
Typically places open around 10:30am, or 11am, for lunch, you'll have to look up the opening times. Normally it's relatively quiet and not too many people are in within the first half hour to hour. I normally like to eat those times, not only less of a wait time, but I feel uncomfortable and depending on how many people can feel anxiety with being surrounded, which can happen in some quick service places, like Mel's Diner for example. Also, I like things on the more quiet side.
I haven't been to Mytho's in ages, so I might be wrong now, but that place was pretty quiet.