Looks like the widening of the A303 (where it passes Stonehenge) is now back on the cards though so there are three possibilities (excluding a flyover fourth :-)

1) A dual carriageway above ground (no thanks, that’s going to increase the speed of vehicles and the noise generated by those vehicles as they whiz past the monument).
2) A dual carriageway tunnel.
3) A dual carriageway bypass.

I don’t know how feasible the latter is but it might be the only viable solution in the end (but wait for the howls of protest along the lines of, “It’ll destroy the environment.” and, It’ll wreck the archaeological record.” No it won’t, if done sensitively and correctly it’ll improve the environment around one of the world’s greatest monuments (which is what we’re talking about) and it’ll no doubt add to our understanding of the archaeological record of the area.