A good place to build mob traps... anywhere, really. The main thing to know is that mobs will spawn in the area around you, so you have to be close, but not too close, to the trap. Look on YouTube for mob traps.
if you want to find a mob spawner download cartograph (mapping and modding) and do a normal map of the world you want to find them in then in the 'only' box type the item number of mossy cobblestone and render it again on normal then open up the 2 pictures ad put them ontop of each other find your base on the full one then switch to the one with only mossy cobblestone and it will show you were dungeons/mob spawners are. if you class that as cheatong just walk around in underground caves for a while