walk down las ramblas in the sun its very trouisty based but you have to see it at least once
eat at la boqueria, worlds best market, the front bit is all stall to buy fruit veg fish etc but the back half has some great small cafe type set ups
wander through the gothic quarter, it really comes alive at night but i would not go in after 9pm as its full of drug dealers and pick pockets (i know i lived there)so between 7-9 its amazing
stop and have a beer outside in plaza real i know again its a tourist bit but its an amazing square and great to people watch for an hour
walk along the harbour area during the day and see all the boats and cross the bridge to the new mall / food area
as for pick pockets…yes its bad but some common sense and you will be fine, dont carry large sums of money or passports, cameras and bags on the front at all times and avoid over crowded areas e.g walk to the far end of the metro platform rather than standing at the start
you will have a great time