Near the Port Of Mobile is the Radisson Admiral Semmes. However this hotel gets mixed reviews and is somewhat worn. We stayed at the Best Western Battleship Inn last year and I cannot recommend it at all.
Mobile is so easy to manuver around that really any hotel in the city is just minutes from the pier. I would pick something along the hotel alley on I-65 inside the city limits - all the chains are there. Just go a little south to I-10 and you will be at the port in 10 to 15 minutes. Signage directing people to the port is excellent.
I personally am quite thrilled to have a cruise ship in Mobile. I hope more will come. It is an easy 6 hour drive for me from north Alabama and the port is really an exceptionally well-run place.