There are a ton of parks in the area that are perfect for picnics of any size. You can find accommodations for 1 to 100 people. I would suggest that you have a take out food picnic at the Courtney Campbell Causeway. If you opt for this choice the benefits are that you can sit in the comfort of you car's ac and you get to listen to the stereo. If you time it right you can watch the sunset or a storm over the water.
Another option available for picnics is to make a lunch and check out one of the many county parks in the region. If you visited a different county park every day you could have a picnic everyday for most of a year before you would visit the same location twice. If you have not checked out the Hillsborough County Parks website, you should. I guarantee that there is a park near you that you had no idea was there.
Sunset rooftop picnics are great too, just look for the tallest parking garage that you have access to and head to the top floor. BOOM Picnic!