Vecrīga (Old Riga) is the historic core of the city and a UNESCO World Heritage Site: a compact tangle of cobbled streets, church towers, and medieval merchant architecture on the eastern bank of the Daugava. It's small enough to walk across in twenty minutes, but worth spending longer — the scale is right for exploration on foot, and the architecture rewards looking up.
The set pieces are well known: the House of the Blackheads on the town hall square, the Dome Cathedral and its cloister, St Peter's with its viewing gallery, and the three medieval churches (St Jacob's, St John's, and the Church of Our Lady of Sorrows). But the best of the Old Town is found in the quieter lanes away from the tourist route — the fragments of the old city wall in Jāņa sēta, the cat-house on Meistaru iela, and the Swedish Gate, the only surviving gate in the medieval city walls.
The Old Town is tourist-heavy in summer — most of the restaurants on the main square are overpriced traps. Head one street back to find better options, or come in the early morning when the streets are nearly empty.