The city of Valparaíso is a very ambivalent city that got poorer and poorer over time. I find the UNESCO inscription a bit difficult to evaluate as the site is mainly the old port area which was one of the richest districts of South America from the 1850s till 1914 and is since then declining (heavily). So parts of the inscription are old, chic houses that formerly were home to rich people and now are home to poor people and that are partially quite rotten.  
 
Nevertheless I enjoy Valparaíso as a city a lot. The street art is excellent and fascinating and with it comes an alternative scene culture that I missed a bit after travelling through Patagonia. Also as a Hamburger I love cities with a port which Valparaíso has and is famous for and which can be nicely viewed from e.g. La Sebastiana, one of Pablo Nerudas houses. The inscribed hills (which means in Valparaíso neighbourhoods) Alegre and Concepción are full of street art and also today touristy and nice to walk through. However the Barrio Puerto which is also inscribed is now a poor neighbourhood with Calle Serrano and Plaza Echaurren. Locals will warn you as Gringo not to run through here. However we took a tour and the guides said that they will warn you mainly because they're embarassed by the apperance of the borough.  
 
The naval museum is full of history and weapons and is to my opinion way too nationalistic and uncritical but that's probably because it's next to the naval academy 
 
The Prat Street and Plaza Sotomayor are very central and you will come across them. You see some old buildings in good shape here however not super impressive. It's a busy town center. Apparently the first bank and post office of Chile were founded here.  
 
As mentioned I enjoyed Valparaíso however not necessarily the WHS part. It's an exciting city however also full of trash, smell, noise and human and dog waste.