If you want your own, I believe I saw one in the buy mode can't remember what category...maybe outdoor? But you can just go to picnic basket in park and grab a plate. That's my sim does cause she stays at the park forever playing her guitar!
you have to go into buy mode on your own lot then go to the lot you want it on and place it, you can pick it up anytime so the lot doesn't take it from you
I'm currently making a movie using one, it's about two nerds that like each other and they spend their days together at the seasons festivals and then they get married and so on I'll post it soon but the quality won't be great, please watch it
If you are building a community lot you can place one of those magically appearing baskets on the lawn or a picnic table so that NPC characters can use them. I don't remember where they are, I think under community objects in build mode.
If you want your sim to ave one so they can picnic anywhere, say while fishing up at te falls, then you can get it as others have mentioned under outdoors when sorted by room. I think you can also get it under entertainment/party item when sorted by category.