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Actually - to reach the start of the Oort Cloud from Earth it'd take around 4 hours. That's 2000 AU. The observer on Earth will see it as about 12 days. This is assuming 99.99% of the speed of light which is completely unrealistic of course.

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Ah I went by the outer edge of Oort Cloud (heck the thing is as thick as our solar system). So 100k AU at 0.99c and got a something on the order of months. We'd also have to accelerate and slow down so this means only if we fly right by earth and then keep going past the destination. If we go by 0.9999c then we're 10x faster and get there in a few days.

Of course, I wouldn't want to slow down once I got to the Oort cloud as it's probably remarkably empty. Maybe planet 9?

The hypothetical Oort Cloud is not a good way to describe a boundary or destination. We only know of circumstancial evidence for it. There have been no direct observations. We believe that it is extraordinarily sparse. Therefore, its beginning and end would be poorly defined.

https://en.wikipedia.org/wiki/Kuiper_belt

Everyone* knows about the Kuiper Belt, of course, but we are looking into at least two other “reservoirs” of TNOs between those named ones.

* https://m.xkcd.com/2501/

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