Thank you for your question. Improving parks and other community facilities is an important task. The Community Tool Box has a nice section on this topic that you might find useful as you move forward.
I agree with your assertion that a powerful visual has the capacity to help multiple stakeholder groups connect with the project. While I cannot provide specific advice on graphic lay out, I would suggest that you consider adding user participation to your process, creating a space and process for the end users to share and co-develop an image that represents what they would like to create. There are several methodologies for doing this that often incorporate visual aspects. Photovoice has been utilized widely to capture user perceptions of assets and needs that can inform design and increase engagement. Creative placemaking and Design Thinking approaches can also be used. In each of these, the end user of the service (in your case the kids and families that will utilize the playground) help define their needs and desires for the space and can use collaborative art, photography, word clouds, etc. to paint a picture that is energizing and reflects their hopes for the space. You could pay a designer a lot of money to develop a beautiful image, but if it is disconnected from user perception, it may not create the type of enthusiasm and engagement that you desire.
Best of luck on your important project.