Please read @Hlitner's comment. His advice is correct, ... as always.
When we were planning our day (9 hrs) on Mykonos, there seemed to be 3 different options:
(A) Mykonos town and Delos;
(B) Mykonos town and celebrity beaches; and
(C) Mykonos town and drive to other parts of Mykonos island.
We chose (A). The public boats to Delos leave from the western side of the Old Port, at 9:00, 10:00, 11:30, and 17:00, and head back from Delos at 12:00, 13:30, 15:00, and 20:00. The boat ride is about half an hour each way.
Delos is a huge archeological site; supposedly larger than any in Greece. You could spend many days or weeks exploring it, but a 3 hr visit will give you a good flavor. Luckily Delos has been relatively well preserved because it did not have and population in post classic time due to limite water, so the local people have not taken apart the monuments for their own use as in most other places. It has been excavated since last 19th century.
Mykonos town is fairly compact, so you don't really need too much time in the town. 2 to 3 hours of wandering about is fine.
We chose not to go for Option (B), because these party beaches (on the western half of the southern coast, from Playa Ornos to Super Paradise Beach), where jetsetters meet, and billionaire's yachts are anchored off shore, seemed just too expensive and crowded for us, and there were much more beautiful Greek beaches at other island. If you want to go there, make sure you read up on the public transport to there (some beaches have bus stops, others don't)
We chose not to do option (C), and not rent cars like we did on other island, because most of the islands that we visited on the cruise were more beautiful than Myconos.