Drop your bags, start in Old Town
If you've arrived by bus or train, leave your luggage at a storage point near the station before you do anything else — Old Town is cobblestones and you don't want to drag a case across them. Then walk straight into Vecrīga: Dome Square, the Three Brothers, the House of the Blackheads, and St. Peter's Church.
St. Peter's tower lift (about €9) is the fastest way to get the whole city in one view — worth it if you're only here once.