For those of us who've never had the privilege of visiting either country, where would you recommend us to go? Any "If you only visit once, be sure to go here" places? Any weird/unique foods or drinks to try?
Some nice ideas already, if i could suggest a route traveling from Düsseldorf i would head south along the Rhein river, first stop Cologne for the Kölner Dom. Then there's Bonn the old German capital, not a must but if you're into HARIBO they're from here and have a nice factory store with way more products than you've probably seen before.
Further south you will find many cute towns in beautiful landscapes and countless castles along the river. You'd also be entering Germany's wine region at a great time of the year, wine harvest, street wine festivals etc.
In Koblenz the Mosel meets the Rhein and the detour of the Mosel to Trier is gorgeous as well. Along the Rhine here begins the Upper Middle Rhine Valley (UNESCO World Heritage Site, outlined on the map i linked) stretching until Bingen. If you have time to go further there's Mainz and especially Heidelberg that i'd recommend.