The easiest way to get your location is to have access to a GPS receiver. When possible, set the unit to read out in degrees/minutes/seconds to save you the trouble of reformatting the coordinates. Mobile and APRS users may want to check out David Lindes's Garmin bulk purchase page for possible deals on a GPS-35. (These are also useful as NTP synchronization sources for your computers that don't move around regularly.)
Barring that, a number of web sites will give you coordinates for cities (or, in the USA, even specific street addresses). The easiest to use is the Getty Research Institute's Thesaurus of Geographic Names. This only gives city-level information, but gives it in an easy-to-read form which can easily be used for LOC records.
Within the USA, Etak and MapBlast! will give latitude and longitude information for street addresses, and AirNav will give latitude, longitude, and altitude information for airports, heliports, and other locations (good for "city" data if you don't want to be too precise about your location!). Australia is covered by the Gazetteer of Australia which includes not only cities and towns, but even railway stations (useful in larger cities for better precision).
For countries not listed above, the Getty Research Institute's Thesaurus of Geographic Names is probably the best resource for low-resolution data (degrees and minutes), but the NIMA Geonet Names Server may have more precise data for some countries.
In some cases, the data are in decimal degrees; to convert to degrees/minutes/seconds, multiply the fractional part by 60 (to get minutes and fractional minutes), then multiply the fractional minutes by 60 to get seconds (and fractional seconds). It's easier to do than to explain!
In the case of the US data, it may be relative to the NAD 27 datum, which is slightly offset from the WGS 84 datum used by GPS and the DNS LOC system. For a sample location in Cambridge, MA the difference was about 2 seconds of longitude and less than half a second of latitude. If you're trying for very precise data, make sure to convert between NAD 27 and WGS 84; you can use nad2nad from the PROJ.4 package to do the conversions.