Showroom Locater App

I'm looking to build an App for a customer of mine, basically when someone download the App into his iPhone and run the App there will be 1 icon that says "Locate Showroom Near Me" and based on GPS and google map it will open google maps and show the showrooms near me. I believe this can be achieved by creating a Map on google and pointing all the showrooms on the map then using the API map key into the App it will pull the locations and locate the closest Showroom next to my current location using iPhone's GPS. i need time/cost for this app including submitting it into Appstore (under my name as outsourcing firm not your name)