Altitude (or depth) can be measured with a barometer.
Latitude is doable, but tricky. Two methods come to mind, but they require staying on one spot for rather a long time to make accurate measurements.
The first option is to use a Foucault pendulum. The rate of precession of such a pendulum is directly related to latitude; the pendulum conveniently serves as its own timekeeping device, so you don't even need a pocket watch to go with it. A protractor and a single-sheet conversion table would be sufficient. You just have to hang around in one spot long enough to get an accurate measure of the precession rate, which would take several hours at least, and while it could be packed down quite compactly for transport, the device would be rather tricky to set up.
The second option is to use a gyroscope. This would be slightly past the level of technology that gave us pocket watches for measuring longitude on Earth, to be able to use spring-driven clockwork to keep the thing spinning long enough, and on sufficiently free bearings. The basic idea is to start the gyroscope spinning, and then observe its apparent axis of precession over a significant portion of a day; the gyroscope will maintain a constant orientation in space while it is transported along by the rotation of the planet. The precession axis is parallel to the axis of the planet, and the angle it makes with the direction of gravity tells you your latitude. It is a good idea to run at least two gyroscopes in parallel, at ninety degrees to each other, to get a better reading, although with sufficient development it is possible to build damped gyroscopes which will naturally align themselves with the precession axis, making taking a reading much easier. Unlike a Foucault pendulum, a gyroscopic device will also indicate north and south--hence the name gyrocompass.
Longitude is much harder. Pocket watches don't do anything for you if you can't measure local solar time. Odometers could be used to assist with dead reckoning. Compasses might actually be useful in this regard as well; if you can establish a depth, latitude, and orientation to true north with a barometer and gyrocompass, and have a detailed magnetic declination map developed on the surface, you could simply consult the table of magnetic declinations along your line of latitude to narrow down options that match your magnetic compass reading.
With a combination of pocket watch and really good gyrocompass, however, you can do better. To make this work, you will need an extremely accurate gyrocompass set rotating at a known position (say, when you enter the dungeon system) exactly perpendicular to the planetary axis. If you were to stay in one place, it would appear to rotate at a known rate as the planet spins, making one full rotation every day, so you can compare its actual rotation with that predicted by your pocket watch. If you stay in one spot, they will match exactly--but if you move east or west, they won't. The difference in the actual position of your gyrocompass at any point from that predicted by the pocket watch will indicate transport around the planet's axis farther or lesser than would be accomplished by the planet's own rotation--and thus, indicates how far you have traveled across the planet yourself. Essentially, the gyrocompass replaces the sun as your indicator of local time, to compare with time at your starting point as indicated by the pocket watch--with slight differences in time-interval-to-longitude conversions since the position of the sun tracks, well, solar time, while a gyrocompass tracks sidereal time.