Traveling from Canada, we arrived in Southampton the day before our cruise to make sure there weren't any issues with delayed flights. We spent the night at the Premier Inn, 6 New Road. It wasn't the closest hotel to the pier but everything else was full by the time we booked. However, the hotel was perfect for a one night stop over, close to the shopping areas, restaurants and parks. If you are looking for a hotel near the port, go with Novatel. It is directly across the street from the dock.
We booked a taxi the morning of our cruise and it never showed. We spoke with several other people waiting in the lobby for taxis, some who had arranged for taxis the night before. Those taxis never showed either. There were 6 cruise ships in port that morning and it made sense that all the taxi drivers would rather be at the port getting the larger fares than the small fare they would get from us. We decided that we would walk the distance. We had two suitcases that were on wheels and the walk was completely flat. It took us about 15 minutes to get to the port.
Boarding was seamless. The only small issue for C&A members was there was only one person at the gold boarding area and anyone platinum and above had to wait in that line up. Once we reached the front we were sent through the platinum + line. It wasn't too bad since we were there early enough and the line was fairly short.
Cabin was quiet since foot traffic in this area is at a minimum. Close to the theatre and right next to the elevator and stairs. So easy to quickly pop back to the room if need be. Would definitely ask for this room again.