Free live music.
Big book stores with coffee shops or local restaurants often have live bands on weekends which you can enjoy for free. Buy your date some coffee and a cookie and you'll still pay less than you would at fancy dinner sans music. Here you can enjoy the tunes and each other's company all at once.
High School Musical.
Attend the local high school for their musical drama event and you never know what you will find. It won't be Broadway, but it'll be sure to be entertaining, affordable and admission goes to a good cause. Plus you could probably start to reminisce about your own experiences with musicals and love of drama when you were younger and learn more about each other than you ever imagined.
Concert.
Sometimes the obvious is just undeniable. Concerts are a great and fun way to have a date. It's an intimate setting to sway to the music together, eat some great concert food and make some memories over your favorite music. If you know there is a concert your date would enjoy, it is a very thoughtful date idea but not a cheap one either. If your theatre has lawn seats available, those are your best bet, because then you two can share a blanket and still get a good view and sounds of the show while spending the least amount possible.
Whatever you do on your date, if you involve music you are sure to have a great time. Music is essential to our society and it has been bringing couples together since the beginning of time. Remember to have fun with it and be yourself. Don't be afraid to sing off key and dance to your own beat.