Manchester Central Library re-opened in March 2014 after a £48m restoration, which transformed it into a modern, digital research centre. You can watch films for free, enjoy free wifi, and use computers (and do some gaming), as well as research, study and borrow books. Loads of events on, too, from live music to festivals.
All of Manchester's libraries have restricted and changing opening hours due to ongoing coronavirus restrictions; check with individual libraries for opening times before you set out.