You'll be missing out if you park and don't drive anywhere. The park is very large.
Here is the map. Look at the 'Dune Climb' - that's the major dunes and it would be a long hike. Also, the 'Scenic Drive' is a must.
May can be cold there. DHDay is a nice 'dry' campground but we love Platte River C.G. (mainly because we volunteered there for 9 seasons along with 3 season on South Manitou Island giving lighthouse tours). It's a very special place for us.
The whole peninsula is gorgeous with neat little towns to poke around. You have to drive to experience it.
https://www.nps.gov/slbe/planyourvisit/upload/SLBEmap2015park_web.pdfhttps://www.nps.gov/slbe/index.htm