I second the recommendation of "Zoo in the Sky" The book is beautiful and one my daughter has long enjoyed.
"When the Moon is Full: A Lunar Year" provides beginning information about the legends behind the name of the full moon each month. In my family we have a tradition of planning a dessert around the names of that month's moon each month.
A few other fave space books:
What's Out There? by Lynn Wilson
A Child's Introduction to the Night Sky
There's No Place Like Space by Tish Rabe
Me and My Place in Space by Joan Sweeney
Several etsy sellers have wooden board puzzles featuring the phases of the moon.
You could build a rocket or mission control center out of boxes.
Cutting out circles and providing finger paint for moon, sun, and/or planet painting might be a fun activity. A printing activity with bingo markers could be a neat way to illustrate the moon or perhaps the various phases of the moon. Glow in the dark paint could add a fun touch to such activities too.
A glow in the dark moon bath is an idea I've come across on Pinterest several times, along with space themed sensory bins. I've also seen star jars (http://creeksidelearning.com/2012/04/15/star-jars-and-so-much-more-learning-about-the-life-of-stars/) and a variety of other activities that have been pinned and completed in my home. Many can be adjusted to be more age appropriate and enjoyable for various ages.
Several years ago my daughter attended a class at the nature park during which the children were given a pan of flour and marbles to throw into said pan. When the marbles hit the flour, the flour was dispersed in such a way to demonstrate how craters are made on the moon.
There are moon globes that are the perfect size for small hands and also moon and earth globe combos--sometimes in beach ball form--which can be fun to play with while also providing a glimpse at the size different between our planet and moon.
NASA has a Kids Club website where a wealth of information can be found: http://www.nasa.gov/audience/forkids/kidsclub/flash/index.html
And, most fun of all, get outside and observe. My husband purchased a "first telescope" for our daughter when she was around 2.5 to allow her to explore the tool and learn to use it responsibly before a better telescope arrived on Christmas a few years later. With that said, a telescope is not necessary for many observations and 2013 will likely prove very 'astronomical' for the naked eye with Comet C/2012 S1 shooting through the skies later this year and some other excitement throughout the year.
Astronomy Magazine's website provides fun observation tools called "The Sky This Month" and "The Sky This Week" where you can keep up to date on the latest happenings in the sky. (http://www.astronomy.com/News-Observing/Sky%20this%20Month.aspx)
On SkyMaps you can download and print a map every month showcasing how the sky will look in your hemisphere during the evenings: http://www.skymaps.com/
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