La Porte
I will preface this with the fact that I have never flown to the Indiana Dunes. I grew up outside of Chicago, and my Father had a summer home when he was a kid in La Porte, Indiana. We went there until I was 5 or 6, then we bought a summer home in Sister Lakes, Michigan, which isn't too far over the border. So, I have been to the Indiana Dunes a lot. I have flown the area a couple times, both out of La Porte (KPPO). It is a nice little field, maybe 10 minutes flight to the lake shore. That said, Michigan City (KMGC) is closer to the Lake and the Indiana Dunes. I'm not sure about rental car access, but you can call and see what they can do. A lot of airports out that way have an airport car with the keys in it, and they just ask you to put some gas in it. Michigan City also has much more to see and do. New Buffalo, just to the East, has a great Marina section. I think you can take Amtrak from Michigan City to New Buffalo. If you go, have dinner at the Stray Dog, and ice cream afterwards at Oink's Dutch Treat.