The Gaelic form of Dundee is Dùn Dèagh - 'the fort of Daig'. Daig was a fairly uncommon Irish name meaning fire. However, Conall Corc, the legendary King of Munster, was exiled in Scotland in the 5th century, and one of his sons was named Daig.
There is a hill rising to a great height on the north of the town, called Dundee Law, and sometimes the Bonnet Hill, from the long street or straggling village that stretches a great way up its side, being inhabited, formerly, chiefly by the makers of men's bonnets, such as we see in London, worn by the Highland soldiers. This manufacture, from the general introduction of hats, in imitation of the English, is now greatly on the decline.
p272 of 'Travels in Scotland, by an unusual route (vol 1)' by William Thomson (1807).
Directions - it's fairly impossible to miss the Law from anywhere in Dundee, and generally speaking, if you head directly towards it you'll find your way up it relatively easily.
And more detailed directions - the easiest way to approach the Law is on the A923 (Coupar Angus road) in Lochee, from where it is sign-posted with brown heritage signs. Assuming that you're coming from the centre of Dundee, head out on the A923 towards Lochee, and just after you pass the steep turn-off onto Ancrum Road to your left, you'll spot a "Dundee Law" sign pointing right up Loon's Road at the traffic lights. Take this road, and when it curves round to the left, turn right onto Byron Street, and then right again up Lawton Road (still following the signposts). At the top of Lawton Road, turn left onto Law Crescent and then after a short distance right up Law Road, which will take you to the summit of the Law. There are loads of paths criss-crossing the Law which will take you to the top, and several places to park the car if you'd prefer to walk the last bit, but there's also space to park at the very top too.