I must be missing something... I have unlocked 4/10 on the underground and can't seem to progress further. I just have a dead end near the projector door and a locked door near the green dragon. I drop through and unlock one door near the green dragon only to be presented with another locked door that is locked from the other side and this seems to be the only way to the other parts of the city. When I look at a map online it shows another path leading up from the room with the projector puzzle but all I see is a brick wall in game.
Is it possible to find another entrance topside I haven't discovered yet and start from another point? Am I missing something to get passed the locked door next to the green dragon or something?
You missed the path to Beacon Hill/etc. North of Dragon Tavern entrance, there's a cell with two doors you interact with - one of them is a simple "O" to open; the other has to be unlocked from behind. (See highlighted region @ http://i.imgur.com/WvXEq.jpg)
There's a drop shaft in the corner - you'll have to dump your lantern and navigate in the dimly lit tunnels. Along the way to next exit you'll have to solve other navigation puzzles similarly - drop lantern, climb wall; drop lantern, jump one wooden posts; etc.