The city of Barcelona is very accessible for wheelchair users. Most of the public transportation has been made wheelchair accessible, all museums and public spaces are accessible and many of the interesting architecture have been adapted.
For a traveler with special needs however I recommend you to use a specialized agency to get the appropriate accommodation, get help organizing your transfers and use an expert guide to show you the city.
Barcelona-Enabled offers these services and more. The services are completely personalized to your wishes and needs.