We landed in Barcelona before our WBTA in 2010. We didn't use a tour operator, but found it was really easy to navigate the city, even with 3 kids and my mom with us. The first day we used the Hop-On, Hop-Off bus which picks up at about 15 stops in a continuous loop, and there are two loops. You got a really good sense of the city, and it was easy to see what things we wanted to return to another day. We visited Park Guell and found it a lot of fun. There was a lot to explore, but getting there was a good walk from the closest bus stop and a bit of an uphill hike. There was an ice cream shop in the park for a nice break.
We also went to the Aquarium Barcelona on a rainy day and that was fun. It was near a mall that had a fair amount of choices for food. The highlight of that excursion was the security guard who let my kids ride his Segway! We also visited Sagrada Familia, and the Picasso Museum which was really interesting. We also went for tapas, and just milled around different neighbourhoods.
It is a city with a lot of purse snatchings I was warned, so I bought a PackSafe Bag and kept it close. We had no problems, but pick-pocketing is very common.
Barcelona was interesting, visually beautiful, and a wonderful city to visit. We stayed at the Hotel Praktik Rambla - it was clean and functional, and very IKEA-inspired on the inside, and full gothic vintage on the outside.
Hope that helps!