The two appeared to be on good terms with each other, reported E! Online.
The two went shopping together and then grabbed coffee and pastries at Paradise Bakery in the city, according to an eyewitness.
"They seemed very cordial. Friends are with them. Kate's brother is there too. Overall, it looks very friendly and not romantic," an eyewitness said.
To make things more clear, Hudson has NOT been wearing her engagement ring throughout the trip.
Hudson, 35, and Bellamy, 36, became engaged in April 2011 and have a son born in July 2011.