Go from San Telmo Bridge to the bridge called Puente de la Barqueta (Calatrava). 30 minutes.
When you get there, follow Calle Resolana to the Macarena neighbourhood. It's one of the most populated areas in the city and there you'll find a mix of churches, convents, bars and coffee shops of all kinds. The arch next to the Basílica de la Hermandad de La Macarena used to be one of the entrances to the city. Some of the remains of the 2nd century wall are still visible.
Go back down to the river and take Calle Pacheco y Núñez del Prado to the Alameda de Hércules, one of the liveliest areas in the city. We recommend Corral de Esquivel (Alameda de Hércules 39) for a beer or soft drink (1.50€) at an outside table (order inside, which is worth seeing). Although it is not particularly famous for its tapas (2.40€), if you're hungry we recommend the "empanadillas" (tuna/meat pasty), the "tortillón" with tomato and bread cream, and the "albóndigas de choco" (chocolate meatballs).
