Exploring Barcelona

Dear IN Barcelona Members,
I'm excited to be heading to an urban yoga retreat in the heart of Barcelona during mid July...please advise me of must do's to best explore the city! I also plan to take advantage while there and visit Valencia..what would be the best way to get there, possible accommodations (safe, clean & affordable) & must dos?
Your advice will allow me to best plan my visit. Gracias!
In appreciation,
A.