Orbitally, Uranus is the closest planet to Neptune. Its orbit is 1.62 billion miles away from Neptune's orbit. However, until Pluto was downgraded from planetary status in 2006, Pluto's orbit was the closest to Neptune's at only 1.42 billion miles away.
Orbits do not necessarily indicate the distance of one planet from another. Because the planets orbit the sun at different speeds, they are often much farther away from each other. For example, if Uranus is on the opposite side of the sun from Neptune, the two planets are 7.36 billion miles apart. Therefore, the closest planet to Neptune varies depending on where the planets are in their orbital cycles.