I encouraged my sons to approach summer/part-time work like this:
1) Get a job with a local company, regardless of what it is (assuming it's legal, of course) and what it pays (assuming at least min wage). An entry-level teenager shouldn't start out in the "I only work jobs that interest me/pay $X.00 per hour/have Y schedule" mode. Learn to show up on time, be respectful to bosses, coworkers, and customers, and give an honest day's work when you're on the clock. Be attentive to detail, even in tasks that aren't your favorite. Learn the details of every position in your business. Be dependable. Seek out opportunities to grow in your job and demonstrate initiative. Teens who can do this in a fast food job will do well in the future when they're trying to meet sales numbers, meet project deadlines, or manage employees. You have a lifetime for specialization. You need a good foundation now.
2) In your free time, find out more about who you are and see how you can grow that knowledge into income. Identifying your strengths and weaknesses and figuring out how to parlay that into income takes time, but not so much time that you couldn't already be earning along the way. Budget your time like you should budget money, and you will have plenty of time in the summer to work part-time, socialize, and learn about yourself.
Hundreds of successful, small businesses start this way---working a job while learning a skill and then expanding that skill over time into a new job. You can waste an entire summer "discovering yourself" and not have a dime in your savings account at the end. Do both of these tasks well, and you will have both earned and learned---never a bad proposition for a teenager.