Unable to get textarea value with LockerService

The value property of textarea has just been whitelisted and should be available next week.

See my comment above but if you want a functional workaround - which is also more in line with the direction Lightning is going in general - you could use the built-in ui:textarea component and bind an attribute to its value. Then don't use jQuery at all to get its value but just fetch the attribute using component.get.