Most Spanish destinations for DL are very reasonable. Malaga might be good for your familia. I've been once, but I think our season will be over early Oct.
Re Korea--there is a large network somewhere online for homestays. Don't recall the name, tho. I think it sounds fascinating.
Gautemala and the lake would be most interesting with the "mystic" atmosphere and volcanoes. Towns/villages accessible by local boat service or by car. Or you can take chicken buses from GUA to Antigua (coffee plantations and colonial museums, etc) then Panajachel @ Atitlan.
DC sounds like great idea--look at homeaway.com, too. or airbnb.com and the Metro is so easy.
Keep searching and keep us posted!
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