In the unlikely event that you find yourself in the area, this is not to be missed, and you can do it cheaply. If you are on a Hurtigruten or other boat, there will be a trip from Honningsval by coach, and you will be stung for a ridiculous amount of money for the three hour trip (£136 on Hurtigruten), but perhaps you just have to do it.
The coach winds through stunning but barren scenery, you may make a stop at a "traditional Sami village", complete with non-strokable reindeer and souvenir shop, before going on to the Cape. Once there you have to pray for good weather.
There's the globe marking the point, a large indoor hall with cafe, large souvenir shop, exhibition, "light hall" and Thai chapel, but the main thing is to have been there.
To note that the climate varies hugely (lots of wind, especially), so dress up warm even in the summer. In the winter vehicles move in snowplough-led convoys, which must be fun!