The Vanderpump Rules star, 36, shared a look at the pair's time at Vitello's in Studio City, California, on Wednesday, when they enjoyed an evening at the Italian restaurant's jazz nightclub, Feinstein's.
Posting a photo of her wine glass and view of the stage on her Instagram Story, Shay wrote: "Date night! Thank you @tomsandoval1 for the awesome seats!!!!"
Shay uploaded a video of the engaged couple listening to the Pandemonium Big Band play, and also provided a glimpse at their meals.
Davies proposed to Shay in July on the balcony of their Los Angeles home. He popped the question with a 12.74-carat rectangular pink morganite ring, which was designed by Kyle Chan.
"I knew it was coming soon, but I didn't know how or when. I was so surprised!" Shay told PEOPLE last month. "Brock knows me so well and knew exactly how to do what I would want."
Shay confirmed that "there's no date set" just yet but they have a location in mind for their big day. "Our dream would be to get married in Bali," she said. "That's where we first said 'I love you.' It's a special place for us both!"
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News of the pair's engagement follows the birth of Shay and Davies' first child, daughter Summer Moon, in April. Their little one's arrival came after Shay previously suffered a miscarriage.
"@summermoon, I will always and forever love you endlessly and protect you," she wrote on Instagram at the time. "You have changed my life 🤍 #happymothersday to me and all the moms out there."
Shay added: "To the moms who have lost children, and those who have lost their moms my heart goes out to you today and always."