I don't know why nobody mentioned satellites and space debris. A piece of something that is manufactured could stay in the orbit for a long time. But, if it's too small, you need to correct the orbit. There is some discussion on SE about making satellites stay in orbit for a long time, see here the discussion on orbit correction, and here the one on making long lasting satellites.
A civilization could build something on an asteroid already orbiting the Earth and leave it there for the next civilization to discover. That will be big enough not to need orbit corrections, and if you coat part of the asteroid with glass or aluminum, it would be visible from Earth. That mysterious space object will always be a puzzle for the generation to come.
Also, if you are advanced enough, build pyramids on the Moon and put metal plates on them, so they shine. They won't be discovered easily, but they will last millions of years. Or you could go all out and sculpt the Moon like in Greg Bear's book Eon.