I d look at Hotels.com or similar
we had a small boutique Hotel near old town,but can t say I d stay there again.Sorry,but plenty to chose from.Try to get near that area to walk around and see,esp.Las Ramblas,port area,etc.
Also, Parc Guell and all Gaudi bldgs. and La Familia church.We took a bus tour with cruiseline then went off on own after seeing the hi points.Get a good guidebook and easy to see on own .
Great city,love to spend more time there.ALso ,google tourism for it.Lots of info.