The main tourist area is within easy walking distance of the port. Lots of great restaurants and cafes, bakery shops and tourist souvenir shops.
We were told to leave our valuables on board and take care to keep an eye on your wallet while in port. We didn't have any issues, but we did notice that the police/security were very visible in the touristy areas, presumably to warn off any pick pockets.
Spanish is the main language and while there are some who speak a little English, don't be surprised to find many places where English isn't understood. We found a beautiful little pastry shop where the elderly lady behind the counter didn't understand any English. We managed to order by pointing at what we wanted, us speaking English, she responding in Spanish. My husband ordered some sort of cake and the woman looked at him and said "No, no, no," and a whole bunch more in Spanish as she pointed to a different cake. She obviously was telling him that his choice wasn't as fresh as what she was pointing out. He went with her choice and was very pleased. We sat near a fountain outside her store and ate our goodies. She was watching us eat and my husband in his limited English looked inside and told her it was wonderful. She was obviously very pleased. All in all it was a great experience.
Main Street is about a 10-15 minute walk from the dock. There is lots of shopping and restaurants in this area.
You can walk to Moorish Castle by going up the Castle Steps. You will need to purchase a ticket to the Nature Reserve (I believe it is 10 pounds) if you wish to see the castle, the great siege tunnels or the apes.
If you only want to see the WW2 tunnels, you can purchase a 0.50 pound walker's ticket. The tunnels are only a few metres further up the hill. This tour is run independently and you will have to purchase a ticket at the entrance. The view from Jock's Balcony is worth it!
If you want to skip Main Street and go right to the cable car I suggest you take a taxi.
Tourist area is within walking distance of the port. I purchased the shuttle ticket but the bus ride was only five minutes.
Las Ramblas is a busy tourist street lined with shops and restaurants. It will also lead you to the Gothic Quarter where you will hear some of the best street musicians you have ever heard.
The Colon Monument at the beginning of Las Ramblas has an elevator inside that will take you to the top for a fee (credit cards accepted). The elevator is small (3-4 people max) and the space at the top is limited. I would think that at most 10 people can be up there at once.
Seafood is the most common food. Be prepared for some unusual choices such as octopus. If, like me, you prefer chicken, you'll have a hard time finding it in a paella. I found it in only one spot - an Irish pub!
There is a shuttle bus service directly outside the pier (2.50 euros) or a water taxi (2.60 euros) if the ship is docked on the opposite side of the old town. If the ship is docked on the same side as the old town, you will be right in the heart of the city when you disembark. It is possible to walk from the opposite side and it will take about 20 minutes or so.
Be sure to check out D'Alt Vista for amazing views of the ship.
Restaurants are plentiful but most don't open until 11:30 am or later.