is eager to move on with her life, a source close to the singer tells PEOPLE, and she's not shying away from the public spotlight.
"She's out and about now," the source tells PEOPLE. "She's not hiding at this point. She's trying to get her life back in order."
Adds the source, "She's trying to figure it all out. It's going to be hard."
As evidence of her desire to move forward, the singer – who got back together with boyfriend Chris Brown
after he allegedly assaulted her – has been quietly stepping out on both coasts.
On Saturday, Rihanna headed to dinner in New York at Da Silvano in the West Village with three people. Over pasta, she "was relaxed," according to a fellow diner. "She looked fantastic – every bit the superstar. But she did look rather serious."
While in the Big Apple, Rihanna also went to the Spotted Pig on Friday night. Accompanied by Brandy, the R&B star met up inside with Jay-Z and Beyoncé
and "looked happy," according to a source.
Last week, the singer hit the town
in Los Angeles, where she celebrated her belated birthday with girlfriends. The following night, she headed to the Geisha House with a group of pals. According to sources, Rihanna "was in very good spirits" during her night out.
Reporting by K.C. BAKER, JENNIFER GARCIA, LAURA HAHN and ALYSSA SHELASKY