Something about viewing the moon keeps beginners and experts alike always coming back to look for more. On a clear night, even from the most light polluted area, our nearest celstial neighbor gives us a close-up view of an alien world.
The moon should always be your first target, as it's easy to find and allows you to familiarize yourself with your instrument while still getting the full enjoyment of using it. Learn to explore the moon instead of just looking at it, the rewards are amazing.
Oh, and a quick note, none of the equipment left behind by the apollo missions is detecable with an Earth based telescope, regardless of the size.
The key to exploring the moon is to do it when it's details are readily apparent. The worst time is a full moon. The line where light meets dark is known as the terminator, and this is where the action is. Mountains, craters, ridges, all cast varying shadows on the lunar landscape.
Follow the terminator for hours, and watch the changing views. A big help in exploring the moon is a good lunar map. Start by identifying craters, and look for more and more detail as you progress.
The first time I looked at the moon through a telescope, I was so awestruck by the view that I didn't notice many of the details I detect now. The moon is an excellent training ground for your eyes. See if you can find Mare Tanquilliitatus (The Sea of Tranquiltiy). Does this name ring a bell? It should, this is the landing site of Apollo 11. It was a thrill for me just being able to identify it.
Explore the craters, can you see the ridges running along the sides? The craters themselves change almost by the hour as the terminator progresses.
Keep notes of what you can detect, you will be amazed what details you can detect over time that you were completely unaware of.
The moon is one of the few targets where you can push your scopes magnifications to the limit, typically around 50X per inch. At 100X - 200X the view is simply breathtaking.
If I were a poet I could probably more aptly describe the views poosible of the lunar landscape. See for yourself this magnificent sight. Share the view with others, there's nothing like hearing the wows and oohs and aahs of folks getting their first (or 1000th) view of the moon through a telescope.