Katy Perry was in the Hamptons solo this week, but will spend a romantic July Fourth holiday there with John Mayer, we hear. On Tuesday, our spies saw Perry walking with a bike in East Hampton, then shopping at the Alice & Olivia store, where the sartorially adventurous singer bought some summer duds, including jeans. We hear she was prepping to spend the holiday with on-again boyfriend Mayer. Perry appears on the cover of Vogue’s July issue, and told Anna Wintour’s fashion bible, “I was madly in love with him. I still am madly in love with him.” In June, she reunited with Mayer and was seen with the crooner at a Friar’s Club event honoring comedian Don Rickles at the Waldorf-Astoria.