Lake County, Indiana, borders both a county with a population over 5 million (Cook, IL) and one with a population under 15,000 (Newton, IN).
In a similar vein, the most populous county in Colorado is not in the most populous metro area. El Paso County surpassed Denver County.
I started thinking about this more and was curious which other states had their most populous county not in their most populous metro area. When dealing with multi-state metro areas, I'll use the portion of the metro area in the state in question.
Colorado - Most Populous County - El Paso (Colorado Springs), Most Populous Metro Area - Denver
Connecticut - Most Populous County - Fairfield (Bridgeport), Most Populous Metro Area - Hartford
Maryland - Most Populous County - Montgomery (Rockville), Most Populous Metro Area - Baltimore
New Hampshire - Most Populous County - Hillsborough (Manchester), Most Populous Metro Area - Boston (just the NH counties)
North Carolina - Most Populous County - Wake (Raleigh), Most Populous Metro Area - Charlotte
Tennessee - Most Populous County - Shelby (Memphis), Most Populous Metro Area - Nashville
Texas - Most Populous County - Harris (Houston), Most Populous Metro Area - Dallas/Fort Worth