We are planning to stay in Rio for three days prior to our cruise sailing on January 3, 2015.
Any suggestions where to stay in Rio so we can enjoy the city and also have convenient commute to the port?

Anywhere in the Zona Sul would do. Most tourists stay in Copacabana or somewhat more expensive Ipanema, both by the beach and not too far from the major sights or the port (which is close to the Centro).
Be prepared for sticker shock when you start to research hotels. Rio is very expensive.

Rio certainly is expensive. Two years ago (before our cruise) we stayed at the Sheraton Rio Hotel. Location (i.e. safety) was a consideration. There is a favela (slum) in the hills behind the hotel, but it was far enough away.

Regarding the commute to port, go to Cruise Critic and join the "roll call" for your specific cruise. It just may be that one of the passengers is organizing a bus to the port. That was the case for us and it was both a convenience and a monetary savings.

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Vic's travels: http://my.flightmemory.com/vogilvie

The Sheraton is quite inconveniently located IMO, far from the tourist sights and isolated from any walkable neighborhoods with restaurants, shops, etc, unless of course you want to explore the Vidigal favela, which some hotel guests do. You would almost certainly want to take a taxi in and out to sights because of distance and probably also to beaches other than the hotel's.
There is, btw, a hostel for foreign and domestic travelers located in Vidigal, with visitors regularly coming and going without problem, so you might want to revisit your preconceptions of what that community might realistically be like.
If the OP were to stay in Copacabana, a taxi to the cruise pier (Maua) might be about R$25 (about U$11), not such a huge expense and certainly a time savings over going from hotel to hotel picking up various other passengers all over town.

Hi,
I agree with SambaChula Sheraton is not the best location so I indicate Acapulco Hotel, Olinda Hotel, Mar Palace and Benidorm. They are four stars hotels with fair prices.
If you have any doubts be free to contact me.

Note: Do not expect the star rating, as it applies to properties in Europe or US/Canada, to be equivalent in Brazil.