If you begin or end in Barcelona - do yourself a favor and add at least 2-3 days for this city alone - it is terrific. It's like Venice without the canals. If one day is all you can manage then do the on-off bus tour but be prepared - the lines are long to get on at Las Ramblas.
As for Athens, it was my least favorite. There are a couple of obvious things to see but the city is not worth spending a lot of time or money in.
Can't help with the others.
Barcelona - the ship docks right by the entrance to Las Ramblas and yes, it is a great walk. Make sure you stop at the food/meat market, down one of the side streets off Las Ramblas. When you hit the end, purchase a ticket for one of the city sightseeing buses (hop on/hop off). You'll get a great overview of the city in English and can get off/on as you please all day.
Dubrovnik is a wonderful city - do this on your own and talk a walking tour around the old city. Walk the walls around the entire city for absolutely breathtaking views! When you finish, have a bite to eat at one of the outdoor on the main square or do some shopping. There is a highly reviewed liquor store that sells local fig brandy, a nice gift or a momento of your trip when you return home. Also, if you walk the entire main square to the water where the boats are docked, there are local women who sell handmade lace by the pier and all the way down to the very end, an outdoor seafood restaurant overlooking the water.
Santorini can also be done on your own if you're the adventurous type. Take the cable car to Fira, then hop on a local bus to Oia - they run frequently. The town is small -one main street, with colorful shops. Venture down some of the side alleys toward the water for stunning vistas and photos.
Back to Fira and have a drink or a bite to eat at one of the cafes on the waterfront (most of which offer great views, expensive prices, and not very Greek food, You will see the entire center of the volcanic crater and views of the ship tendered. It's gorgeous. Or take one of the side roads and check out one of the few local restaurants in the area still there for great Greek food -Cafe Nicolas. Nick will translate the daily menu for you.
Many sidestreets and shops to browse as well.
Athens -if you've never done it, take a tour to the Acropolis! If you want the benefit of a tour guide, take the ship's tour; you'll learn a great deal. If you want to do it on your own with a self guided tour, then walk from Piraeus (about 1 1/2 miles around the edge of the crescent shaped port) to the metro stop and grab the metro to the Acropolis stop. It's easy, fun and very safe; the metro is beautiful -the stations kind of like museum stops, with all the exhibits. You can change $ to local currency (Euros) at HSBC a few steps out from the Piraeus port. It helps to have an HSBC account so bring your ATM card. In fact, I opened a small account with them at home before I left to have this flexibility since they have many branches around the world (tho not in Italy).
All of the info above can be obtained by reading Frommers, Fodors, or Lonely Planet travel guides. Most likely your public library has them or check their online sites.