This Riga travel guide, and any Riga old town guide worth following, sticks to what holds up on foot. That's Old Town's medieval core, the Art Nouveau district beyond it, and the day trips that make sense once those two are covered.
Riga's Historic Centre joined the UNESCO World Heritage List in 1997. The things to do in Riga that actually hold up are almost all inside or just outside that same protected core.
Nearly everything in this guide is walkable from Town Hall Square. That's why so much of it stacks into a single day without ever needing a taxi or tram.