What are some best practices for creating an online office locator?

You can also just match the first five, failing to four, failing to three, failing to two digits of the ZIP code. Faster and less prone to the fuzzy weirdnesses of maps. People prefer a choice, anyway. The "closest" by formula is often not the one that a user FEELs is closest, or that they'd prefer, since "Oh look that one's near Rob's house" and "that one's right on my way to work" can't happen if you're too dictatorial with a "find closest" approach. Be fuzzy, show many options, let users decide which is really closest and most convenient to them. It's more human-friendly.

No, adding the two differences is no good. I think you should be using the http://en.wikipedia.org/wiki/Haversine_formula. There's a good Javascript example http://www.movable-type.co.uk/scripts/latlong.html that you can probably convert. One sevice that does free zip to position conversions is http://geocoder.us/, although I haven't used it.

You can get lat/long out of google using their geocoding API, but be warned, it sometimes gives insane results. You might do better to grab the center of each zip code from somewhere more reliable, and then if you want to do address level location, do the google geocoding, but throw away the result if it's more than N miles from the known center of the zip. (Seriously. Google likes to tell you that your address is in some different continent.) For the actual sorting, you don't add the distances, you use http://en.wikipedia.org/wiki/Great-circle_distance. If you don't understand that page, look for great circle distance, haversine formula, or earth distance and your favorite programming language. It's a well-solved problem, so you shouldn't have to trouble yourself if you don't understand the math.

If you're in a small state, the great-circle distance is all but equal to the 2D distance. Just saying. Unless a user of your website really cares whether the office in Istambul is (a bit) closer than the office in Caracas, who cares?

Please allow people to view a full list of addresses. Sometimes people don't know the ZIP (traveling or looking for someone else).

Thanks for the feedback. I am planning on having a zip code search, and a drop down list with all of our locations. They will have multiple ways to search for offices. The search results will also show multiple locations, so they can choose which one "feels" closest.