Ahh I'm so sad I just found this question! Five months too late. Haha
But if you're still looking for ideas, it would be cool if you went to a designated hiking/forest/tourist area. That way you could run around and hide out in the woods like in the actual games, while still being close to civilization. Many places allow you to camp nearby, so you could have your actual party and cake at the campsite.
Although having a giant cornucopia would be incredibly awesome, it might not be practical. Instead, try constructing your own tent style artillery unit from old bedsheets and long sticks. For weapons, you could use various play toys like nerf guns and even duck tape daggers; all the fighting and killing effect minus the blood!
You could have all of your guests wear certain colors to represent the twelve districts, so you'd pair up two people for each district. ( a fun twist would be that whoever RSVP'd first would be from a lower district, so they could get better gifts from their sponsors (parents) throughout the games.)
I'd imagine that the whole games would take a few hours, so if you started around 3 o clock, depending on where you live, it would start the get dark just after you were done.
Once the games are finished, you could return to the campsite for cake, presents, and of course a campfire :)
*** keep in mind, walkie talkies are a great idea to have handy, that way you can help prevent someone getting lost!