Music lessons are just one of those things that is great for a person on so many levels! Yes, the obvious reason for music lessons is the fact that you will learn to play beautiful music, but learning to play an instrument is also so beneficial in other aspects of your life (or your children's lives) as well.
Starting with the easiest to see first. Learning anything is great for a person of any age. Growing and improving yourself is never a bad thing. Exercising your brain, while training yourself to focus you'll be enjoying the benefits of this, and your children will also be applying this focus in other aspects of their lives as well (school). It is amazing how many parents of children I teach tell me how their grades have been improving since taking music lessons.
Learning an instrument is a great way to immerse yourself and introduce your children to the fine arts. Starting kids in music lessons young is a great way to develope an interest in classical music for them. It is amazing the difference of children starting early in piano lessons around 5-6 years and my students who begin taking as teenagers. The younger ones tend to enjoy the challenge of learning classical music.
Learning an instrument is very soothing to yourself and those listening to you. Music tends to be something that can instantly change your mood when you hear it playing. Great music can get you to feel what the composer was feeling when he wrote his music - or her. Many adults who are looking to take music lessons tell me they are wanting something for themselves after stressful days of work that can be therapeutic for them. So the chose to take up piano or guitar lessons as a way to grow in something new, while it being something that was relaxing to them. There's a reason they play classical music at spas.
Playing an instrument gives people a way to express themselves. There will never be a day when someone says, it has all been written. Sometimes feelings can not be expressed or fully conveyed by words. Sometimes I think we don't even know what we are feeling. Music gives us an outlet to convey or feelings and emotions outwardly when words can not be found.
Everyone has their own reason for wanting to learn an instrument. The great thing is, it doesn't matter, they are all good reasons, because learning to play an instrument is good for you. And a big perk, you're just going to be that much more awesome becoming a musician.