SportTracks might be an option. They have an online and an offline version, and free trials. I don't know if the offline application ends up exchanging any data with an online server, though.
You could also use RunningAhead. It's online, but they're not using your data the way Strava is. It's not a for-profit website. Just supported by donations and a lot of volunteer programming hours. It can sync with a Garmin watch pretty easily, but any other watches will require a manual upload of the .fit or .gpx file. While it lacks the slick look of Strava and some of the more modern logs, it's rock solid and is pretty much designed to be everything a serious runner wants in a log, with nothing they don't.