As an example of some of the gee-whiz stuff you can uncover at The Degree Confluence Project – by referring to this North America map’s page and this Tennessee map’s page I found:
and rounded that to ** 36°N 87°W** or 5.6 miles (9.0 km) SW of Bellevue (Davidson), Williamson, TN, USA
Approx. altitude: 209 m (685 ft) which makes better sense if viewed on this map (if zoomed out sufficiently) 
{For reference the next “confluence” near my place is this one}
Anyway, using that as a starting point and going due N, S, E, and W to find the first non-USA point in each direction I learned:
N: http://www.confluence.org/confluence.php?lat=50&lon=-87
26.0 km (16.1 miles) S of Aroland, ON, Canada
http://www.mapquest.com/?q=50.0,-87.0
Latitude: 50. Longitude: -87.Thunder Bay, Unorganized, ON Canada
NE of Thunder Bay
S: http://www.confluence.org/confluence.php?lat=21&lon=-87
18.1 km (11.2 miles) WSW of Alfredo V. Bonfil, Quintana Roo, Mexico
http://www.mapquest.com/?q=21.0,-87.0
Latitude: 21. Longitude: -87. QR Mexico
SW of Cancun
E: http://www.confluence.org/confluence.php?lat=36&lon=-6
20.6 km (12.8 miles) S of Cabo Trafalgar (Cape), Andalucía, Spain
http://www.mapquest.com/?q=36.0,-6.0
Latitude: 36. Longitude: -6.Barbate, AndalucíA Spain
SW of Barbate
W: http://www.confluence.org/confluence.php?lat=36&lon=140
2.4 km (1.5 miles) SW of Nakayara, Yawara-mura, Ibaraki-ken, Kantō, Japan
http://www.mapquest.com/?q=36.0,140.0
Latitude: 36. Longitude: 140.常総市, 関東地方 Japan
S of Joso
NE of Tokyo
I’m not advocating this amount of work to locate those surprising geography trivia things, but it is fun!