Hi Katie!
We just got back from a trip to Santorini, and we hiked from Fira to Oia. There's one main path everyone takes, which for the most part, runs along the caldera side. Check out Santorini Dave's info on the hike. We found it very helpful, although we encountered a lot of people hiking the trail from both directions. According his site, it take 3-4 hours. We're photography nuts, so it took us 5, lol. It won't take you nearly as long starting from Imerovigli. Wear shoes with really good traction, though. No flip flops! Saw one girl in them and felt bad for her. A lot of the path is cobbled, some paved, a lot of it is neither, especially between Imerovigli and Oia. There were sections that ran up- and downhill with very loose gravel - like, we had to dig in our heels with every step; otherwise, we'd slip. I wore capris, and dark shoes, and my legs and feet looked like I went through a dust cloudt by the time we finished. But we enjoyed it very much as well as the incredible views along the way. The closer you get to Oia (somewhere between Oia and Imerovigli) you cross that narrowest point of the island where you can easily see the ocean from either side. Pretty cool. You can take the bus back (K-TEL) and ask the them to drop you off in Imerovigli. It costs 1.8 Euros pp, and it runs about every half hour (someone collects payment once you're on the bus). The bus station is a few blocks behind the Church of Panagia of Platsani. (If the links works, zoom in, and you'll see a pin for the bus terminal.)
As far as the sunset goes, Imerovigli, is supposedly the 2nd best place to watch the sunset. We watched it from Oia the first night with hundreds of other people. It was hazy, and you wouldn't have been able to see the sun dip into the ocean. We bailed before the sun finished setting, because we knew that as soon as it was done, the hordes of people crowding the walkways and narrow staircases would leave at the same time. You could always try making a reservation at a restaurant with a view. The following night, we enjoyed the sunset from our hotel terrace in Fira, which had a wonderful caldera view and zero crowds.
Hope this helps and have a fantastic time!