I call my multiple-choice campaigns "sandboxy" rather than "sandbox". I have one like this currently, an episodic Classic D&D Karameikos campaign.
My 'actual sandbox' Wilderlands campaign does not have 'adventures'; it does have 'sites' - locations such as dungeons where adventure is particularly likely. But the PCs aren't required to investigate all or any of these. It's also notable for the ability of the PCs to go anywhere & do anything adventurous and it will run smoothly, there's never an adventure of the week that the PCs must do - not even a choice of two or three. Sandboxy games are choice matrices; genuine sandbox games are completely open. Both are distinct from linear games like the Pathfinder AP I just finished, but they're quite distinct I think.
There was an old White Dwarf article that discussed "Scenario Design" vs "Environment Design". Sandboxing involves "Environment Design" - you create an environment for PCs to explore, not scenarios for them to play. This is why my Karameikos game is not a true sandbox - the PCs are presented with adventures & adventure options each week. Whereas in my Wilderlands sandbox there is the environment, in which exist such locations such as the Halls of Tizun Thane and the Caverns of Thracia, but the campaign is not 'adventure driven' - NPC quest givers don't, as a rule, come over to the PCs and ask them to do X. Rather the PCs roam the world encountering interesting stuff, and there are dynamic NPCs doing likewise. A lot of my sandbox effort goes into detailing tons of motivated NPCs whose behaviour interacts with the PCs and with each other. The world is a web of interaction; more detailed in the immediate campaign area, but thanks to the Wilderlands of High Fantasy Box I can look anywhere in the world, see who's there, and have an idea what they're up to.
Read more: http://www.enworld.org/forum/showthread.php?471441-How-I-Sandbox#ixzz3pqOQkn2H