Using the PHP Core SDK, the main way of accessing file content is using the getFile method, or for images where you don't need the full resolution, the getThumbnail method. However, these return the data directly, e.g., to save on your server and serve back to the user, so that doesn't suit your needs as described.
It sounds like you'd prefer the API to return a link to the image that you can use as the source for the images in the HTML of your page. The Dropbox API doesn't offer a method particularly well suited for that, but there are some non-ideal options:
1) You can use createTemporaryDirectLink to get a direct URL to the image. Note that these links expire after four hours though.
Using it would look like:
list($url, $expires) = $client->createTemporaryDirectLink("/default.png");
2) You can use createShareableLink to get a preview URL for the image. These links don't expire. Note that these don't link directly to the image data though, so you'd need to modify them as documented in this help article.
Using it would look like:
$url = $client->createShareableLink("/default.png");
Also, not that both of these are subject to bandwidth restrictions, per this help article.