Astronomy is exceptional fun for children and adults alike as well as an educational activity. In the Caribbean, I do education programs for visitors and schools alike, usually on the beach away from all the lights.
Further north, Spring is one of the best times as the weather is warming up with few winter storms and yet the nights are still cool enough to where the insects aren't a problem. Unfortunately, unless one is near a large city, visiting a planetarium isn't easy and can be expensive. Fortunately, once the lights are turned out, there are options for backyard astronomy projects for kids.
One easy project is to have them start monitoring the sun, the earth's closest star. Drive a large stake in the ground and then have the child measure the shadow each day at the same time. The shadow will shift and change through out the year. This can help the child understand the changing seasons, the night time stars will be shifting just like the sun, but is often harder to distinguish. The really creative can build a sundial!
Another lazy project is to build a few hammocks, you could spread out blankets but the ground can be cold, damp and filled with ants. Then go out at night with them facing the same position and have the child mark the relationships of stars due to season and time of night. Teach them the myths associated with the constellations, story telling always entertains children. Star charts, known as planospheres, can help with this but it is best if they see it themselves. When they find a star, not on the planosphere, it is either a comet, a planet, or a satellite.
Once they start learning the stars and constellations, build a theodolite. Attach a long pipe or tube in a fixed location, mark out all the degrees of the compas and the have the child sight on stars and planets. The kid will learn about angles of declination and eventually be able to tell direction using the stars, they will never be lost again!
Now that the child has learn about star identification, celestial movement, angles it is time to consider some equipment. Start with binoculars as they are easier for first time users, have numerous uses, and can be used in those hammocks. They are also cheaper than the telescope. Some small galaxies, the moons of Jupiter, and the craters on our moon are all fantastic to view through a good pair of binoculars. When the child wants to see more, then get the telescope!