PEOPLE's Celeb Style Council member also showed off the beautiful sparkler from her fiancé, an onlooker says

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It was a lovers’ getaway in Palm Springs, Calif., for Jamie Chung and Bryan Greenberg over the weekend.

The stylish starlet and her new fiancé spent Saturday afternoon lounging poolside and packing on the PDA at a Coachella Music and Arts Festival party held at the Guess Hotel.

“They were hugging from the side and holding hands while sitting on neighboring floaties in the water,” an onlooker tells PEOPLE. “They would often give each other forehead kisses. They were cute.”

Hanging out in the VIP lounge, PEOPLE’s Celeb Style Council member showed off the beautiful sparkler from her actor love to fellow partygoer pals Jesse Metcalfe and Cara Santana.