There is nothing quite the same as seeing live entertainment. Whether that entertainment is a Broadway show, a ballet, or a live sporting event, being at the show/game in person is just better than watching it at home.
I love taking my kids to see shows. Many theaters offer family packages and/or $10 tickets to shows. The tickets at that price are limited, but they give you the opportunity to share the experience without breaking the bank. We are fortunate, that in addition to regular shows, that we have been able to take in shows geared towards children. We have seen groups like Imagination Movers in concert, a local Children's Ballet group perform Fancy Nancy and Madeline ballets, storybook shows such as If You Give a Mouse a Cookie and Wrinkle in Time by a Professional Theater Company for young audiences and families, and shows like Disney on Ice and Phineas & Ferb Live. Each of these experiences can be used to teach children about the arts and to see familiar things transformed into live performances.
The holidays can be a great time to give someone the gift of show tickets (and sporting event tickets). Many theaters, having thought of this too, will send out their annual performance information just in time for the holidays.
Sometimes, you are able to get the tickets in time to wrap them and give them, but other times you can not.
At my house, if we can't get the tickets, we have been known to print out "gift certificates" that we make saying that we are giving the gift of the show. I have also done this for sporting event tickets.