If you want a more local food experience go maybe to union market, bunch of casual places. Or check out H st NE?

Also as a Muslim I can tell you, you basically never have to worry about places that have pork as their main staple. I'm sure they exist but it's nothing to worry about.

Though it's hard giving recommendations without knowing more of what you want.

Also because you'll be here in fall and have time maybe check out some more scenic places out of the city like Shenandoah national park or Harper's ferry WV.