Summertime means big-budget movies followed by belly-busting dinners. And The Street, a new complex that is a re-concept of the Chestnut Hill Shopping Center, has emerged as the newest food-and-flick destination. Opening within days is the Showcase SuperLux, a cinema that serves a full menu of food and cocktails right to your plush, oversized seat. The theater will have its own outpost of the locally based, upscale Italian chain Davio's Cucina. It joins several other high-profile dining openings on The Street in recent months, including Treat Cupcake Bar and Boston’s first Shake Shack burger joint. Coming soon: a Del Frisco’s steakhouse.