Valparaíso is a very unique city in that there are many ways to get where you need to go. This is partly because most Chileans do not own a car and also because the city is very hilly and spread out along the coast. Valparaíso is actually famous for its public transportation system that has been continuously operating for over a hundred years. Which form of transportation you want to use depends on where or how you want to get there. It seems like most Chileans try to avoid walking very much so you can get almost everywhere you want to go via public transportation. It's just all about finding the right form of transportation going the right direction.
The first option for getting around are the Ascensors which are a series of semi-vertical elevators that allow people to get up into the neighborhoods in the hills without going up thousands of stairs. These are actually considered national monuments in Chile and are quite famous. They are very old, beautiful and somewhat terrifying, as the whole wooden cart shakes as it slowly rolls up the hills. Many of these are no longer functioning but they are always a great and scenic way of going up if you have the opportunity.