Personally I would not rent a car at all. The reason your cruise ship stops at Chania is because of the wonderful experience one will have wandering around a medieval old town and harbour.
Just take the bus or a taxi to Chania and enjoy the city.
However if you do want to use the car you can drive to Elafonissi. It is probably a 2 hour drive along the coastal road. Three if you use the interior mountain route.
While Balos is closer you are not allowed to drive your rental car on the road to Balos. You invalidate your insurance the second your tires turn onto the road. There is a boat excursion but it won't be back in time for you to get back to the ship.
If you want a shorter drive than Elafonissi you could go to Falasarna. It is a string of nice beaches. It also has an ancient site. If you have an I phone there is an app that recreates the site.
Other places you could consider are the archeological site at Aptera just 18km east of Chania or you could continue to Rethymno to explore the Fortezza. It also has an old town like Chania. But if you want to see an old town just stay in Chania. Chania also has a beach which is a 10 minute stroll along a tree lined seaside road west of the city walls.
Perhaps images will help.
Western Crete http://www.flickr.com/photos/stanbr54/sets/72157632115757899/
Chania http://www.flickr.com/photos/stanbr54/sets/72157632117917828/
Theotokopoulou St area http://www.flickr.com/photos/stanbr54/sets/72157632118491316/
Gramovossa, Balos Elafonissi https://www.flickr.com/photos/stanbr54/albums/72157698932695812
Ancient Aptera, Melidoni Cave and village.
https://www.flickr.com/photos/stanbr54/albums/7215767211837963