This article is written for you. Because every picnic spot near Kolkata that ranks on Google right now is a listicle of fifteen names with no phone number, no package and no answer to the organizer's real questions. Here is one spot with all three: Mayer Bari at Namkhana, by the Sundarban delta, with a fixed full-day package, in-house food, and a phone number that picks up. 
