Ferry from Mykonos to Santorini (Thira)

Greek ferry schedules aren't usually published more than 2-3 months ahead. You probably won't see a June schedule until late March or early April.

The schedules for the ferries between Mykonos and Santorini have remained basically the same for several years now and there's no reason to think there will be any significant change next season. You'll have at least a couple of different options. You can take the 10am highspeed catamaran, the Seajet2 to Paros (40 minutes) and catch the large conventional Blue Star car ferry when it stops at Paros at Noon on the way to Santorini, arriving around 3:00pm. Or you can take the Hellenic Seaways FlyingCat4 leaving Mykonos at 3pm, arriving at Santorini around 6:30pm. The FC4 has "No sailing" days a couple of Wednesdays every month. Once that schedule is fixed you can see it here, sometime in April: http://www.ferries.gr/hfd There may be other options as well, but in early June these two are the most likely possibilities. All ferry schedules can be found here once they've been made 'official': http://www.openseas.gr/OPENSEAS/index_en.vm

Can anyone give an approximate cost for this ferry?

You can see the costs for the FC4 here: http://www.ferries.gr/hfd The option involving Paros and 2 ferries will be less.