We were there in April. It’s a wonderful place to stop.
The first thing to “not miss” is the gift store. I’m not kidding - it’s one of the very best I’ve ever seen. Pick up a guide book to all of the side altars, chapels and grottos. There are so many, you can’t hit them all.
See the main sanctuary. If you don’t have time for a tour, the guidebook will help you focus on some of the most spectacular images there.
Go to the Crypt Church. That’s the lower level. Besides the Church itself (where there is Mass almost every hour it seems) there are several chapels and some beautiful statues. There is a section there with items from Blessed John Paul II and from Pope Benedict’s recent visit. Pope Paul VI’s tiara is there too.
Again, use the guide book to narrow down which chapels to see based on your own heritage and spiritual interests. For example, there is a side altar to Our Lady of the Rosary and one to Our Lady of the Miraculous Medal so if one of those is a special devotion to you, find it. There are chapels funded by Irish Catholics and Vietnamese Catholics (among many of national/heritage ones) so you can match up to your own heritage. There is something with the Knights of Columbus (I think it was the carrilon) so if you are a Knight (or married to one), that might be something you want to see.
Have a great trip.