South Point on Hawaii's Big Island is actually the US's most southerly point. The Hawiians call this rugged place Ka Lae, and it is thought that this was the spot where the first Polynesians stepped ashore.
Bone fish-hooks dating back to the third century AD are the oldest archaeological finds, but by far the most interesting are the petroglyphs. Petroglyphs are now most commonly referred to as "rock art", but these carvings were an important way of recording for posterity everyday events such as fishing as well as the great dramas of birth and death.
The easiest way to get out to Ka Lae is in one of the hire cars that can be rented through Alamo (tel 0800 272 200) from the airport for pounds 25 per day.
Moving to the other end of the compass, the US's most northerly extreme is in the state of Alaska. The small town of Barrow (population 4,000), has the largest Inupiat Inuit community in Alaska, and one of the largest in North America.
Despite the modern-day conveniences, such as public transport and brick houses with central heating, Barrow's traditional outlook is symbolised by the town's annual spring whale hunt, where everyone is expected to lend a hand - or a harpoon.
Any schoolchild can grab an atlas an tell you that chilly Barrow is 330 miles north of the Arctic circle, but did you know that this is the place where US humorist Will Rogers came to an untimely end? The plane carrying Rogers stalled and crashed into a river just south of the town shortly after taking off.
Most Americans visit Barrow to say they've been to the top of the world or to view the midnight sun between early May and August.
The best way to see Barrow is to book a trip with Alaska Airlines (tel 800 468 2248) once you are in the United States. Prices start at pounds 250 from Anchorage, which includes an overnight stay in the Top of the World Hotel.
According to the US embassy, the most westerly point in the USA is also in Alaska: the remote island of Matignak (179 6' west). The last inhabited place however is Adak Island, about 100 miles to the east of Matignak. Both are rocky outcrops of the Aleutian Islands, which are strung out like smoked herrings from the Alaskan coast. The furthest west anyone can get on mainland Alaska is a windblown place called Wales, but as a matter of fact the American public don't seem to be interested in these Alaskan outposts.
The most westerly inhabited place on mainland USA is the Alaskan town of Nome. Most people see Nome as a grimy, treeless place in the middle of nowhere, full of tatty houses with front lawns strewn with old bicycle frames and abandoned refrigerators. This image, however, belies the town's exotic history.
In the summer of 1898 some Swedish gold prospectors struck lucky in Anvil Creek. By winter the news had reached the gold-hungry fields of the Klondike, and by 1900 Nome was declared the largest city in Alaska with some 20,000 residents.
Today's population is only around 4,500, but the residents still all have a contagious gold-rush fever. From the prospectors who ply the beach to the honky-tonk saloons, it's clear the place has retained its rough frontier appeal.
Nome is connected to the outside world by daily flights with Alaskan Airlines (tel 800 468 2248) from Anchorage International Airport. Ticket prces start at around pounds 200 return.
Moving swiftly eastwards, the last extremity on the other side of the US is Lubec, in Maine. As far as I can see the town has very little to do with Lubeck (the historic trading port in northern Germany, famed for it's marzipan). Lubec, Maine, is actually a smelly commercial fish-processing centre.
The town's main claim to fame is that Franklin Roosevelt's father James bought some land here in 1883 and built a palatial summer "cottage". The future US president spent many of his boyhood summers here, and was later given the 34-room cottage.
If you have a desperate urge to go there you should first catch a plane to Boston. There are regular flights from Boston to Bangor, Maine, and from there numerous buses make the three hour journey to Lubec. Heading east from here, the next stop is Land's End, Cornwall.