Do you know this drama?

Early 2000's Japanese drama. Aired in California on local Japanese stations. Probably around 2003-ish. Didn't air with subtitles.

The main motifs were that a woman traveled around place to place and seemingly was writing letters to someone. Seemed woman-centric. Each new episode showed her at a new location. There wasn't any huge romance in the drama. Seemed like slice of life?