I dislike having to keep going back to the ship to click the next ocean tile. Is there any way to set it to auto explore and forget about it?
There is no auto explore button as there is with protecting trade etc.
However you can define multiple destinations by holding down the
shift key whilst plotting your course. This allows you to select multiple ocean tiles. Therefore you can customise the course you wish a ship to take over the coming weeks/months by selecting lots of different destinations in one go.
The same applies with land units.
For Naval units there is also the Patrol option. Which once selected will cause the ships to repeat their orders in a loop. This can include docking at a friendly port for repairs.
A combination of using the
Shift Key to stack orders and plot your desired course and then using the Patrol option to repeat those orders can be very handy and make Naval operations such as exploring a doddle rather than a chore.
I use this a lot when exploring, by making a ship sail up and down the same stretch of coast line over and over again. Then leaving him to it. You've just got to mindful of the ships attrition and make sure it visits port for repairs regularly enough.
Update - Limited to El Dorado DLC only
As @Max stated, you can now order fleets with explorers to automatically explore uncharted territories and coasts without taking attrition.
"Fleets with an explorer and at least 3 light or heavy ships (or a mix of both), that are in a port can undertake exploration missions such as exploring a sea, charting a coastline and circumnavigating the globe. When on an exploration mission, they do not suffer from attrition and cannot divert from their course."
@Max is almost correct, however, there was a issue with the tool tip that stated you need three light ships and three heavy ships with an explorer. This is not true, you need three light ships OR three heavy ships with an explorer.
I also advise against going for the circumnavigation as soon as you reach dip 9, it's a sure fire way to lose you ships and your explorer (50 dip worth and at least 60 ducats).