1. Climb Skaros Rock
Skaros Rock is beautiful and it's not a difficult climb at all for a moderately experienced hiker/climber. That being said, there is no safety anything - no signs, no ropes, no fences, no guards. That adds to the majesty of the experience but you should also be careful. The winding trek up Skaros is pretty easy until you get to the very top. Then, you have to really climb and it's not a place you'd want to fall. When I went, a German couple was ahead of me. The woman was unable to make the final ascent to the very top of Skaros rock, which is a flat expanse of rock from which you can stand and drink in the horizon and the Aegean Sea. It's soul shattering (in a good way). The man scrambled up. I followed. The getting up was easier than the coming down. The German left the top before I did and when I started to lower myself down over the edge, I saw he and his partner had waited for me to make sure I was able to get down ok and offered help if I needed it. They were incredibly nice. This is just to say, be nice, offer help, and be careful. Don't climb alone. DO NOT buy tickets to tour Skaros Rock. There is absolutely no need. It's a waste of money and you will get a much more soulful experience out of exploring it yourself. It's just going up and down - you're not going to get lost.
If, as I recommended in my Part I, you stay in Imerovigli, you should take the easy hike to Fira one day - it's a half day adventure but you could turn it into a full day easily. Fira is a touristy little area chock full of street vendors, museums, churches (including the gorgeous Catholic Cathedral of Saint John the Baptist, which is definitely worth a visit), shops, and restaurants. Finding a vegetarian restaurant was challenging, but I found the locals were easily able to adapt dishes to remove meat for me and the amazing wines and rich beans, herbs and vegetables made everything a pleasure to dine on. The walk to and from Fira took a long time for me not because the distance was great but because the views were spectacular. I kept stopping to just drink it in. Each moment was better than the last. More on Fira here.
If the views between Imerovigli and Fira were great, the views on the hike between Imerovigli and Oia were spectacular! The Oia trek is several hours and some of the ground is really stony and gravelly so wear good hiking shoes if you want to be comfortable. The hike itself is a wonderful adventure and then you can take the opportunity to explore Oia. I hated the touristy part of Oia, with the marble ground and uber expensive shops - it just seemed a little gauche. But, that's easy to skip! Just stay local. The restaurants are great. I highly recommend Floga, which has wonderful food and gorgeous views if you dine on the terrace. If you go, my absolute favorites from the menu were: the Greek salad, Santorini fava beans puree, the traditional Santorini tomato dumpling with basil, the steamed mussels, the wild mushroom risotto, and their fresh fruit platter. More on Oia here.
4. The Sulphur Springs and a Day Long Boat Trip Around the Caldera Bay and to the Volcano
Generally, the island is small and easy to navigate. You don't need to pay for tours and I wouldn't recommend it - it would take away from the joy and spontaneity of discovering the island for yourself. That begin said, I would recommend spending money on only two things: a sail around the Caldera Bay which takes you to the volcano and the sulphur springs and a tour of the wineries. Learning about the volcano is pretty cool and the Caldera Bay is incredible. Experiencing it from the water as well as from the land is breathtaking. The sulphur springs are super touristy but if it's part of the boat ride, jump in and check them out. To know in advance: the sulphur will dye all your clothes brown so DO NOT wear a white swimsuit or anything you don't want to turn a bit rusty in color and don't wear any jewelry. The "hot" springs are also not hot. At best, they are tepid. Also, if you're asthmatic or pregnant, don't go. The sulphur can cause health issues for you. Last, know that the boats can't anchor in the springs; they anchor a little bit away so you have to swim out to the springs. It's not that far but it's enough that if you're in bad shape or not a good swimmer, it's going to be more scary than fun for you. There will be really sharp rocks just under the water as you swim up to the springs, so just be aware of them. More on the springs here.
5. Winery Tour
As I mentioned in Santorini Part I (the food), the wine - particularly the dry white wines - of Santorini is famous and the fame is well deserved! I'm going to quote Greeka.com here because they say it better than I can:
"The volcanic soil and the special climate of Santorini give a unique taste to the local wine. The wine of Santorini was famous all over the Mediterranean basin in the ancient times and even today it is exported in many countries of the world. Vinsanto, Nychteri and Mezzo are just some of the local varieties that can be found in many restaurants on the island and in various cellars in the world. A very special thing to do on the island is visit some of the many Santorini wineries, spread all over the countryside. Most wineries in Santorini are actually found in the central and the southern part of the island, in the villages of Mesa and Exo Gonia, Megalochori and Messaria. Large vineyards surround the wineries, which can be visited individually or in an organized wine tour. The most famous Santorini wineries are Santo Wines and Volcan Wines." Source: www.greeka.com. Click here for details on multiple wineries in Santorini.