Despite of Barcelona’s quite big size, it is easily explored by foot. We needed to use public transportation only to Guell park, that was worth it, as walking distance here is already quite long. Other places, as Rambla, Citadel park, Montjuic, so on are quite in walkable distance, but church of Saint Family and Hospital Sant Pau I guess could be harder to reach by older people or simply at very hot days, so when needed to use metro or bus from Catalonia square.
Walking is always my favourite way to see cities in Europe. So that was the same as well here in Barcelona. It was very easy to navigate around the city and to find the attraction sites just by walking. Of course, visiting during the middle of the summer, we had our outdoor gear that is needed, that is shorts and sandals :)
Barcelona is a city that can be seen on foot, at least the majority of tourist areas. Walking the Ramblas is a must- about a 1 mile walk which lands you at the beautiful harbor. You can easily walk to the Barri Gòtic neighborhood from here as well as other quarters. We felt pretty safe walking around during the day and really did not have any problems at night although I didn't feel as secure outside the touristy area as some of the other European cities I have been to.
Barcelona is a big city and some important sights are far from the centre, so that, it's necessary to take public transportation. However, the best way to visit a city, is on foot. The city has many streets and avenues that deserve a walk, let alone the heart, the Gothic district and Las Ramblas.