I've talked about random map tricks before, but I'm not sure if I've done anything restricted to d6 rolls, kept as simple as possible (no dice map/drop dice techniques, easily memorizable so that you don't need to consult a table...)
Generic Tower and Dungeon Expander semi-random dungeons. In a long corridor like the one in the pic, roll 3d6 for each side of the corridor and keep only one die out of every set of doubles or triples. The remaining dice, in order, are what's behind the door, using a simple d6 "table" expressed as a map. (I've modified the room order for this example by making a result of 5 = the Tunnel and result 6 = the Staircase.) Optionally, at the end of the corridor, roll 2d6 and use one die result if you roll doubles, otherwise leave it as a dead end.
Gridmapper.) Result 6 is a staircase. Roll another d6: on 5+, the ladder or stairs go up, otherwise they go down.
How many tunnel segments you need to create a seed map is mostly a matter of taste, but I'd say three would be a decent start.