Dimitris Taverna has the best grilled fish on Santorini. I don't know how he does it but I haven't found anyone who manages to grill the fish with such flavors like him, and I have been to most Taverns here (I live in Santorini since 20 years now! ).
Read my post for a lot of more info: tripadvisor.com/…48659422
Santo Winery has a stunning view but not the best wine. Here is a good site for all most wines Santorini has to offer (except Art Space which has a small and excellent production): http://www.winesfromsantorini.com/
Oia is generally packed with tourists during sunset, specially at the old castle but in June it will still be ok to watch the sunset from up there. In June the sun will set later and more to the right side of the island so you have to be high up to see it all! You can walk down to Ammoudi afterwards for dinner at Dimitris Tavern, or drive down. I also recommend Pirgos for sunsets since you will be able to see both sides of the island from up the castle. Have lunch afterwars in Metaxi Mas in Exo Gonia which is close to Pirgos but book a table since its very good and very well known!
Edited: 5:00 am, April 12, 2013