Uranus is 2.88 billion km from the Sun.
Neptune is 4.5 billion km from the Sun. Nearly twice as far as Uranus.
Pluto is 5.9 billion km from the Sun on average. It varies a lot, from inside the orbit of Neptune to nearly double the distance - 4.4 to 7.3 billion km. New Horizons will be reaching it at one of its nearer approaches. Pluto is also significantly inclined to the solar plane, unlike the planets.
By contrast Jupiter is less than 1 billion km away: 0.779 billion km.
Saturn is 1.4 billion km -- twice as far as Jupiter.
Note that if you managed to slow yourself down at Neptune on your way out to Pluto, you'd still have the distance from the Sun to Saturn to traverse. Say you cut half your speed -- it would take you nearly six and a half years to reach Pluto, rather than the 3.2 of the current mission trajectory. You're trading speed and time here.
And you'd still have to lose some 20,000 km/h of velocity when you arrived.
Space is big. Really big. You won't believe just how vastly, hugely, mind bogglingly big it is.
Then there's the orbital periods. Neptune's year is nearly 165 Earth years, Uranus is 84 years, Pluto's is nearly 248 years. This means that Pluto, discovered in 1930, won't have completed a full orbit of the Sun until 2177. Neptune, discovered in 1846, completed its first full orbit since only in 2010.
Edit: but only when they also line up correctly, which is why I think it would take hundreds of years of waiting.
Edit2: After watching the linked video, Uranus would be out, since Pluto is never close to it, but Neptune might work at some point in time when these planets are close.