We toured Rome independently as we had been there previously. It was great fun to get a map and wander the streets marvelling at one architecural masterpiece after another. The street food is excellent and cheap. You can get a great panini or pizza "takeaway" (to go) for under $5. Take it to a park or square and have a fantastic al fresco experience! We opted to visit Palazzo Barberini, which houses exquisite masterpieces, and the National Gallery, which houses more of the same. Keep in mind that many churches close between +/- 12pm-4pm so plan that into your itinerary.
We visited Olympia, Olympia Land Winery, a great baklava bakery, the Virgin Mary Monastery, and an adorable seaside cafe with Andrew, Katakalon Taxi. He charges 55E per couple, if there are 2 couples, or 55E each of there are just 2 of you. Great value for the tour.
We had previously visited Athens so I opted to go to the National Archaeological museum having not gotten there on our last trip. You can get overwhelmed by the archaeological treasures, but pace yourself so you don't!
The Plaka offers a great opportunity for shopping, particularly local crafts. Just beware of hawkers who will try to sell you an umbrella or a taxi tour. They can be quite persistent!
We did a DIY walking tour which was very nice. We visited the market, but felt overwhelmed by the vendors who would just not leave you alone no matter what you did or said. The carts selling fresh corn and pretzels are great for quick snacks and at 1 lira, it will only set you back around 70 cents. Be aware that most attractions require cash, so unless you have liras you cannot get in with a credit card.
If you are planning to do a lot of sightseeing, which is likely, you should by the Istanbul Museum Card. It is about $42 pp as opposed to around $55 if you were to buy indiviual tickets to the same number of attractions. They do not make it easy to get the card. Make sure you ask when you get to the ticket booth of your first attraction. It is worth it as many attractions only take cash, and you can buy this with a credit card, AND if you have the card you can skip all other lines at all other attractions once you have purchased it.
You will need small denominations of cash for the JetonMatik machines that dispense tokens for the tram. The tram is easy to use as there is just one line. You can see out so when you see something you like, just get off:-)
We took a tour with AP Tours who took us to Pompeii, Positano and Sorrento for a full day. The driver was knowledgeable and courteous and the van was comfortable. They charge by the passenger so by the time we got to 24, it was 50E pp which was a fraction of what the ship charged. We had a great day, saw some amazing things at Pompeii, and some beautiful scenery on the Amalfi coast.