I found some of those web sites I mentioned earlier today. Hopefully some of
these will help:

http://www.travelinfo.gr/ferryfare.htm

http://www.gtpweb.com/RoutesForm.asp

http://www.greekislandhopping.com/

And since you said you'll be on Mykonos for about a week, this might be
helpful...

http://mykonosholidays.com/

My experience with Piraeus is fairly limited, as I chose to fly directly to and
from Athens from the islands I visited. However, I did take the metro to
Piraeus once for a day trip to Aegina and found the whole process to be
relatively painless. We did not buy our tickets in advance going to Aegina
because we took the slow ferry, but on the way back we took the high-speed
ferry, for which we did need advance tickets (in our case a few hours in
advance).

The slow ferry from Piraeus to Mykonos is about 6 hours if I recall correctly
from reading about it.