Baron Francis Blanchett is an alright sort, as far as Varisian nobles go. He's helped you out of at least one scrape while you were travelling through Korvosa so when the time came when he asked you to return the favor you were willing, at least once he promised to pay you for your trouble. You retrieved some letters with apparently sensitive information in them from a political rival of the Baron. As thanks for your discretion the Baron gave you a sum of gold, an adamantine amulet, an old map, and a letter of authenticity.
"The amulet and map are a pair you see. I took them as payment of a debt some years ago. Wouldn't have taken them but the debtor was my wife's cousin's husband, you know how it is. He had that letter of authenticity from a diviner at the Star Temple so I'm sure it's accurate. Well, as accurate as a centuries old map of a growing jungle can be mind. See those runes at the bottom right there? They say Dostol 48 yun. Now I have no clue as to how far a yun is but Dostol is an old name for Nantambu, a city in the southwest jungles of the Mwangi Expanse. Somewhere between there and this body of water here which I assume must be Lake Ocata is this valley here," he said pointing to the runes at the center of the map surrounded by mountains. "This here says 'Heart of the World' in old dwarfish. I tried to get diviners and historians to tell me about the Heart of the World but all anyone could tell me was that it was old and powerful. I won't tell you not to sell this map and be done with it but I'm mighty curious as to what's at the heart of all this, mind the expression. If you go to this 'Heart of the World' and come back with a story I can tell my associates at the Pathfinder's Society I'll buy back that map off of you for 5000 gold pieces, 10 times what you could sell it for to an antique dealer even if you had Asmodeus's silver tongue."
The easiest boat to the Mwangi Expanse drops you off at Bloodcove, the only foreigner run port city in the country. It's a cut throat city, much like the nearby jungle, but you can find pretty much anything you'll need here to start your exploration.