While US 12 (The Dunes Highway) is the scenic route from end to end, US 20 (Dunes Relief Road) is the quicker road and provides most of the services (gas, food). It touches the southern boundary of the park and provides easy access to all the main features of the park. From US 20, use
1. Lake Street to reach the Douglas Center for Environmental Education & Marquette Park
2. Lake/Porter County Line Road to reach West Beach
3. SR 249 to the future Portage Lakefront Park and the current steel mills
@ SR 149, lodging, food, and fuel (access to I-94)
@ I-94, food and fuel
4. Mineral Springs Road to reach Bailly/Chellburg parking & Cowles Bog Trailhead
5. SR 49 to reach Buell Memorial Visitor Center, food, fuel, lodging (south) and the State Park (north)
@ Ly-co-ki-we Horse Trail
6. Kemil Road to access the Calumet Dunes Interpretive Center trails and Kemil Rd Beach
7. 500 E for access to the Heron Rookery
Town of the Pines
8. IN 520 to US 12 to reach Central Beach and Mt Baldy.
The Lakeshore is traversed by several major highways. The most scenic is US 12, which runs from the west end of the park in downtown Gary to Michigan City in the east. It offers the widest variety of things to see. Along the drive, there is the commercial district of Miller in Gary, West Beach access, Inland Marsh overlook and trails, Long Lake views, the steel mills, access to Bailly Homestead and the Chellburg Farm, Tremont Picnic area, Calumet Dunes Interpretive Center and accessible trail, the Great Marsh,, the Town of the Pines, completed by Mt Baldy before entering Michigan City.
I-94 is the quickest way to get to the park. There are 2 interstates I-80/90 (Indiana Toll Road) and I-94. I-94 is closest to the park. Both have exits on Indiana 49, which leads directly north to the visitor center at the US 20 & IN 49 interchange, then north to the State Park and the National Lakeshore.
The Calumet Bike Trail runs nearly the entire length of the park. It encompasses the entire east end, where you can get from the historic areas of the Bailly Homestead and Chellburg Farm, to the State Park, down to the Visitor Center on Kemil Road and access to Kemil Beach and Lakefront Drive. It terminates just before Mt Baldy. It's a way to get around the park or to have a pleasant ride through the park.
A few cares do need to be taken. Until the trail is linked to the Duneland Trail in Chesterton, there are some narrow roads around Bailly and Chellburg. It would be best to avoid crossing US 12 on weekdays due to the large trucks hauling steel. On weekends the traffic can be heavy. So it may not be recommended for young kids to try using the trail as access around the park.
There are similar cares in Beverly Shores. From the Visitor Center, up Kemil Road to the Beach, the road is narrow and may not be suitable for you children.
The link to Mt Baldy is better in that the road is wider, but the road is also US 12. No big trucks here, just a lot of traffic.
The South Shore and South Bend Interurban Railroad was a traditional method for Chicagoans to get out of the city and to reach the dunes. Today, it is the last interurban, running from South Bend to Chicago. The schedule is designed to serve commuters to Chicago. That makes it harder to use it to get to the park.
On the other hand, it can be a fun trip with kids into town or a museum. You could even ride it a few stops and then come back. (Check the schedule carefully so you don't end up in a parking lot waiting an hour for a return train). They provided family rates on weeks.