Last Minute Afternoon BBQ/Picnic Venue

Hi - wasn't able to find any recent advice on this topic and was hoping someone might have some new ideas. We're looking for a last minute place to host a small gathering (20 adults,10 kids) Saturday afternoon. We'd like to go to one of the regional parks but are concerned there may not be picnic space available unless someone goes to the park in the morning and stakes out a spot until we plan to arrive later in the day (3-4pm). We've called a few parks and most of the reservable space is already reserved.  

Any suggestions on places that may be less crowded? Would we be able to show up at Tilden or Roberts and find space in the afternoon? 

Thanks for the suggestions and advice