03/28/2012 AT 6:00 AM ET
The couple arrived at the W San Francisco, where they stayed in the Extreme-Wow suite. “They stayed very under the radar,” a source tells PEOPLE. “They wanted their getaway to San Francisco to be low-key and secret. It was just about the two of them being together.”
Still, they did manage to get out and about a bit: Spears and Trawick were spotted shopping nearby their hotel at the Westfield San Francisco Centre.
– Ulrica Wihlborg