Ethereal Dark-Side-of-the-Moon Base: Earth has a convenient natural satellite that is tidally locked, meaning one side always faces away. This should serve well to bamboozle the Earthlings' primitive attempts to discover our base, whilst being relatively nearby (as compared to Mars, for example).
We selected a site for the base and quickly started construction. Strangely, we uncovered the remains of an Earthling craft that had been launched roughly 80 years ago- but there are no signs of active lunar missions at present, so we should be good.
The base follows standard patterns; it is made up of interlocking hexagonal buildings which house various facilities. All the essentials are present- generators, factories, cloning vats, hangars, research labs, specimen containment.
The buildings are formed out of alloy frames and walls, covered in bricks made of processed lunar material- causing the base to blend in with its surroundings that little bit better.
Notably, the base is ripe for expansion, as more buildings can always be added.
This look okay for a base description? It's pretty bare bones, so if somebody wants to write a more comprehensive/exotic description, please do. This is intended as a fallback if we can't think of anything better.