Riga is the Baltic city that most people expect to be one thing and find to be three. There's the medieval Old Town of merchants and guilds, where the House of the Blackheads and the spire of St Peter's still define the skyline even though both were destroyed in the 20th century and rebuilt. There's the district just north of it, with around 800 Art Nouveau buildings and some of the most ornate facades in Europe. And there's the Riga of the 20th century, which you meet in a Soviet-built museum cube, a former KGB headquarters and a market housed in old zeppelin hangars.
It's a city of about 600,000 people that you can cross on foot in an hour, and that's why five days works. The old center takes two days if you do it properly, the occupation history deserves a half day on its own, and two of the best things in Latvia aren't in the city at all: the castles of the Gauja valley and the pine-backed beach of Jūrmala. In November, the days are short, with sunset around 4:30pm and earlier as the month goes on, so the plan puts museums in the middle of the day and saves the walking for the hours of light.
Day one is the Old Town, day two the market, the Freedom Monument and the Art Nouveau district, day three the occupation and the KGB building, day four a trip to Sigulda and Turaida castle, and day five the coast at Jūrmala and the Great Ķemeri Bog Boardwalk. The country is covered on the Latvia page. Start on a Tuesday if you can: the Art Nouveau Museum is closed on Mondays, and the order of the days works from Tuesday to Saturday. For travelers going north, Tallinn is the next capital up the coast, and from there Helsinki is a short ferry away.