For a secure LAN for printer, phone, tablet, etc., you'll need a wireless router.
If you are willing to connect phone, tablet, laptop, etc., to the park's Wi-Fi for internet access and to your LAN when you need that network then you do not need for the router to have internet access and, hence, no reason for a wireless bridge. The only purpose of the wireless bridge was for the convenience of getting internet access through the router.
If you are willing to connect phone, tablet, laptop, etc., to the park's Wi-Fi for internet access and to your LAN when you need that network then you do not need for the router to have internet access and, hence, no reason for a wireless bridge. The only purpose of the wireless bridge was for the convenience of getting internet access through the router.