As should be evident from my earlier correction, I found it confusing. Use 'near' as Amy suggested-- although the premise is odd, as people normally picnic at the beach as a location, even though they are not on the sand itself.
Learners who post grammatical but otherwise semantically odd sentences are liable to have the wrong thing corrected for them.
We wouldn't normally say simply 'by' to mean near. We would say 'by' 'near' or 'next to' but I agree it's odd, as you aren't really saying where you ARE picnicking. You don't normally just say you did something near to somewhere without a bit more detail. People still wouldn't have a clue where you were talking about - it could be one of 100 or 1000 place