This page contains an implementation of the Montenbruck and Pfleger sunrise / moonrise / twilight algorithm. The algorithm should work for all latitudes even within the (ant) arctic circles. There will be a 'fuzzy zone' at around latitude 67.43 as a result of using approximate Sun postion routines - and a similar zone around the 'lunar arctic circle' - but real rise and set times depend strongly on your local horizon anyway. Treat any 'days' or 'nights' shorter than about 20 minutes with caution.
If you don't know proper latitude and longitude, click this link, search the place, and select Misc./Export position from menu to fill the form.