Perhaps a short list of speculative mechanisms for future archaeological research would be interesting to produce. 
Ground-scanners, Transparent-Earth (PDF) eyeglasses, metal detectors, 4D earth-modeling environments used to visualize abandoned settlements, and giant magnets that pull buried cities from the earth.
Autonomous LIDAR drones over the jungles of South America. Fast, cheap, and out of control portable muon arrays. Driverless ground-penetrating radar trucks roving through the British landscape.
Or we could install upside-down periscopes on the sidewalks of NYC so pedestrians can peer into subterranean infrastructure, exploring subways, cellars, and buried streams. Franchise this to London, Istanbul, and Jerusalem, scanning back and forth through ruined foundations.
Holograph-bombs—ArchaeoGrenades™—that spark into life when you throw them, World of Warcraft-style, out into the landscape, and the blue-flickering ancient walls of missing buildings come to life like an old TV channel, hazy and distorted above the ground. Mechanisms of ancient light unfold to reveal lost architecture in the earth. 
Or there could be football-field-sized milling machines that re-cut and sculpt muddy landscapes into the cities and towns that once stood above them. A peat-bog miller. Leave it operating for several years and it reconstructs whole Iron Age villages in situ.
Simultaneous milling/scanning devices that bring into being the very structures they claim to study. Ancient fortifications 3D-printed in realtime as you scan unreachable sites beneath your city's streets.
Deep-earth projection equipment that impregnates the earth's crust with holograms of missing cities, outlining three-dimensional sites a mile below ground; dazed miners stumble upon the shining walls of imaginary buildings like a laser show in the rocks around them.
Or a distributed iPhone app for registering and recording previously undiscovered archaeological sites (through gravitational anomalies, perhaps, or minor compass swerves caused by old iron nails, lost swords, and medieval dining tools embedded in the ground). Like SETI, but archaeological and directed back into the earth. As Steven Glaser writes in the PDF linked above, "We can image deep space and the formation of stars, but at present we have great difficulty imaging even tens of meters into the earth. We want to develop the Hubble into, not away from, the earth."
Artificially geomagnetized flocks of migratory birds, like "GPS pigeons," used as distributed earth-anomaly detectors in the name of experimental archaeology. 
[Image: "GPS pigeons" by Beatriz da Costa, courtesy of Pruned].
So perhaps there could be two simultaneous goals here: to produce a list of such devices—impossible tools of future excavation—but also to design a museum for housing them.
What might a museum of speculative archaeological devices look like? A Mercer Museum for experimental excavation?
(Thanks to Rob Holmes and Alex Trevi for engaging with some of these ideas over email).
