Why not move to Pluto?
Here is my attempt at answering your question.
It has the natural resources and the cool weather which would be perfect for an AI in my opinion. The problem is landing there.
Astronomers have detected "natural gas" on the surface of Pluto, in
the form of frozen ice. (BBC)
So robotic AI could definitely make a use of it.
Also, blue hazes and small regions of water ice have been found on Pluto.
Regions with exposed water ice are highlighted in blue in this composite image.
“Large expanses of Pluto don’t show exposed water ice because it’s
apparently masked by other, more volatile ices across most of the
planet. Understanding why water appears exactly where it does, and not
in other places, is a challenge that we are digging into,” (Source)
It is technically feasible to land a robotic probe on Pluto, though it would be extremely expensive due to the need not only to cross the billions of miles between us, but to match Pluto's speed on arrival. New Horizons was a thousand pound probe that took a decade to reach Pluto only to speed past it.
So that might be the biggest challenge. Let's see what future tells us!
The following animation shows how our view of Pluto has changed from
its discovery by Clyde Tombaugh in 1930 through the 1990s and the
latest images from the New Horizons spacecraft in 2015. (Source)
Pluto's distance and small size makes studying it a challenge, but astronomers have relied on advanced optics such as the Hubble Space Telescope to examine the dwarf planet.
Scientists have determined that the planet is somewhere between 50 to
70 percent rock, with ices making up the rest. The surface is composed
of exotic ices such as methane and nitrogen frost, with water ice
lying underneath. Carbon monoxide is also present on the surface.
Recent studies by the Hubble Space Telescope suggest the presence of
complex organic molecules. (Source)
(Source of above image)