Near Foggy Bottom, you might like Founding Farmers or District Commons.
Near the convention center, I like Acadiana--not sure if that would fall under "too expensive" though.
If this were me, however, I'd jump on the blue line to Federal Triangle, have your family member walk or metro to Archives metro, and meet at Oyamel. It's a modern Mexican spot owned by Jose Andres, and they have great lunch specials.
Also, no matter where you choose, I recommend a reservation.