A wholesome everyday sentence. ~を兼ねて attached to a verb or noun means 'combining with X,' 'while also being X,' marking a dual purpose. Here a drive (ドライブ) and eating favorite ramen are bundled into one outing — you go for the ramen, and the drive comes free with it. The ~に行く construction (verb-stem + に + 行く) marks a purpose of movement: 食べに行く = 'go in order to eat.' Note that the に on 食べに is the particle marking purpose with a motion verb, not the locative.