Prayer Walks are always a great idea for an outside event. You can walk through a neighborhood, a business district in your town, schools, nursing homes, almost anywhere and simply pray and speak words of life into that area.
Worship Art made or performed while somewhere like a park, beach, downtown or a similar place is also a good outside event.
Volunteering is a more "public" event where you might work at a mission, a nursing home or school.
Daddy God's Love Tea Party is an outreach idea to girls.
Empty Bowls Project: www.emptybowls.net Potters and other craftspeople, work with the community to hold events that will benefit the hungry.
Teardrop Jar Event: For our Teardrop Jar Event, we made jars with the Scripture regarding our tears in God' bottle (Psalm 56:8) and placed them throughout a couple of local cemeteries just before Memorial Day weekend.
Prophetic Valentines: Make Valentines Day cards and write a word you feel the Lord would want the person receiving the card to know. As an event, go pass them out personally or leave them where people will find them.