Combination your house+ the library+ the playground, for the gt kid who doesn't fit even in first grade.

We have one of those.

We also have a more obviously gifted and definitely more socially able child who is doing ok, bored but not downright depressed yet.
Northern VA. public school is ok for this sort of child, so far. There are several excellent private schools, many specifically for gt kids if you are willing to move or drive, and ok elementary programs in p.s. Mid school specialty programs get very full so it is hit and miss, and movement to very advanced material is very rare (perhaps as it should be?).
High school options range from Governor's schools all day programs to schools with college 1/2 days, and I really think that last is an excellent option.

In a place so close to D.C. you'd think foreign language would be presented earlier across the board, but I think 8th is the earliest it is seen except for a very few schools.