Living in the streets doesn't mean that I should abandon my daily routines and work. The society has still built us libraries which are so far best places to gain intelligence as current schools in UK are not able even to teach writing skills and have implemented supervised prison type environment.
When its raining outside you cant much stay inside shopping centers or stations as security will throw you out. But you can always trust libraries where also the toilets are clean and available.
But to use them properly in Spain, you need a library card. Spanish library cards are useful in any state library so once given to you, its like a NIE (social security) number needed to find any work. But you need a local permanent address and phone number to get it. and there is always ways to talk someone over to give you such kind of card without any verification. If not possible in one library, try another.
For the Internet, all Barcelona libraries have WiFi for clients so you must have a library card to use your laptop. As there are usually very much people using Internet this way, most of those libraries have special WiFi areas or rooms even and you will get free electricity to use and recharge your batteries.
Another way is to use local computers. There is two type of Internet computers: Internet and Internet Multimedia. Internet is containing Web browser only and you cant much save or manage your files. Only few libraries had Web based MSN messenger included to browser.
Internet "rapido" is free to use anyone up to 15 minutes (you can take longer if nobody is waiting for it) and does not need a reservation. But in biggest libraries, you do not have even a chair to sit. Internet needs a reservation, which you can do using Internet Reservation computer usually near by Catalog computers. You can take it by half and hour slots.
Internet multimedia computers are usually located in separate room and have Microsoft office installed besides web browser so you can save and manage your files.
To get access to those, you need to ask reservation.
Libraries in Barcelona are some very small and some in several floors. They work usually 10AM-2PM and 4PM-8PM, but some days they do not have a break, some are open Saturday afternoon even and two of them Sunday morning. My daily life has been to start my trip from one library after the meal from Mother Theresa, getting to another afternoon and ending my day in the third library.

Lets start from Paralello when you will find nice small library Poble Sec Francesc Boix at Blai 34 (paralell to parallelo). They have very few computers at second floor so if not possible to make reservation there, you should continue to parc Joan Miro where is another small nice library of Joan Miro. Its just after the placa Espanya.
If that is closed (open in very odd hours), continue your trip to plaza Saints where you will find Vapor Well after crossing the street which goes to Estacio Sants and will continue to next street up.
Even usually I havenŽt made reservation using them as sitting just to free computer, now I got clear that they have limitation to use Internet only 1H per day and maximum 2H per week.

Sure there is more libraries going upside to Corts but I haven't studied those. In the Plaza Lepps up is one big library called Jaume Fuster which is open sunday mornings (when it has been extremly difficult to get the reservation) and another Sunday morning library is Sagrada Family (near by the most famous church) at Provencia 480. The Sagrada Family is nice big and quiet place to work not so far from city Center.
Going up to the hills, there is nice small library in the Parc de les Aigues.
And my favorite is of course Xavier Benguell at avenue Bogatell (near by the sea where I sleep). Its quiet and very friendly not so far from the city center.
I have checked some other libraries but most of them are small local community centers like Fort Fenc. Vila the Garcia (at the traverse of Gracia) is a nice library even the toilets has been always closed and I haven't yet figured out their working hours.
At least, knowing your libraries and having a catalynia library card, you can feel safe in Barcelona. Especially when there is raining or you have need for the toilet.