I know of a website that lists today's sunrise/sunset times for my town along with the current weather. I can download and parse the contents of that page, but it takes a couple seconds to gather the data. I was hoping for an algorithm, which would be immediate.

Using your link I did manage to find a complete calendar for sunrise & sunset times for my town; I'll see if I can't cobble something together that at least gets me within a half hour of the correct times.

I don't need a ton of precision; I just don't want to be off by more than an hour.