The asteroid belt is the logical place for extraterrestrial explorers to establish a base. And conditions are such there that the base would survive relatively intact even after it was abandoned for centuries, or even millennia--or longer. Sure, it could be camouflaged or hidden if they chose to do so, but it might also be deliberately left to be discovered. It would only require an inner planets species to eventually develop a technology capable of stumbling across it. Think of the "2001" Sentinel scenario. Or maybe the place was just abandoned after they completed their mission here, and no effort made to cover up the site. Whether or not something like this actually happened is something else again, but it certainly can't be ruled out.

Boots on the ground? Absolutely! Even a very old and derelict alien base would have the potential of phenomenal technological discovery for us. Whoever got there first might stumble on artifacts, or perhaps even records, of great economic or military value. In fact, it would not be unreasonable to expect there would be a race to get there, perhaps even conflict; think of the struggle of European powers for control of the spice trade and riches of the East, or the wars fought over the New World, even before its full commercial value was realized. It would jumpstart everybody's space program overnight, and I bet the ships would be armed to the teeth.

The very fact that the alien facility even existed would be a closely guarded secret, but only if it was possible to keep it that way for long. I doubt this would play out that way, though. I believe most interplanetary probes are managed by several nations, and have very extensive protocols for data distribution and sharing. It would be very difficult for any one agency to improvise and implement a credible security program on a moment's notice, much less a total lockdown and cover story a la Heywood Floyd. No one would have anticipated such a discovery and made the appropriate security arrangements ahead of time. The news would leak out; scientists are notorious gossips, especially when they feel self-righteous.

But we can dream, can't we? Just think, this might be one way free enterprise could finally get a jump on bureaucratic government space programs. NASA or ESA would prefer a ponderous and systematic archaeological mission, and the militaries and intelligence agencies of the world would favor secret crash programs. But private enterprise could probably raise the cash, improvise a high-risk mission and beat them to the prize, just like they did in the 1500s. Never underestimate the power of greed.