Venus might be the best alternative given these criteria.
We're going "all-in" here and we need to scale fast, so we should select a location that is as similar as possible to a place where we already have lots of experience.
Roughly 500,000 people are "residing" in Earth's upper atmosphere (by traveling in aircraft) at any given time. Aircraft are already accepted as safe and reliable vehicles.
We could create a fleet of solar-powered flying habitats that would always stay on the sunny side of Venus. (See: https://space.stackexchange.com/questions/65119/could-an-acid-proof-solar-powered-aircraft-stay-aloft-on-the-sunny-side-of-venu)
There are several reasons why this strategy makes sense...
Natural Resilience to AI Threats
On Venus, all computers will have to be installed in the same flying habitats that people live in. It's too hot for servers to operate on the surface; therefore, it will not be possible to set up giant data centers. Power budgets for each aircraft will be tight so it is unlikely that people will want to run power-hungry computer programs such as AIs. This makes it much less likely that an AI would be able to find a place to hide from, or gain the upper hand over, the human population.
Bootstrapping The Colony
Humanity already knows how to build, test, and mass-produce reliable aircraft with carbon composites. It should be relatively easy for us to design such aircraft, thoroughly test them in Earth's upper atmosphere, mass produce them, and then launch a large fleet to Venus.
Space Radiation
We still do not know how well humans (and other species of plants and animals that we might want to bring along) will fare after many years of exposure to space radiation. The remainder of Venus's atmosphere would provide a "free" shield against space radiation. All other options (except a bunker on Earth) would require us to build shielded habitats, limiting our colony's growth rate.
Gravity
We do not know whether humans can reproduce successfully in low gravity. If we need to create habitats with artificial gravity to have healthy humans, this will slow down the growth rate of our colony. On Venus, the gravity is 91% of the gravity on Earth and thus should not pose a significant health risk.
Air Pressure and Temperature
It will be more difficult to build habitats and expand the colony if every new habitat needs to be engineered and carefully manufactured to eliminate the risk of containment failure. In the atmosphere of Venus, at an altitude of 50 km, the air pressure is one Earth atmosphere, so a puncture would not lead to rapid depressurization.
The temperature in the upper atmosphere of Venus is 20°C at 56km, which will make it easier to construct and insulate the livable portion of newly constructed habitats. (ref)
Assuming the aircraft can be slowed down enough, it should be possible to go outside to do repairs on the aircraft's exterior without an insulated, dust-resistant, pressure suit. Something more along the lines of a lightweight hazmat suit should suffice. Possibly two aircraft could dock together while flying which would allow one aircraft to be powered down and serviced or refurbished while the other provides propulsion and lift.
Executive Decision (1996)
Power
Without a reliable long-term power source, the colony's survival would be at risk. Solar power in the upper atmosphere on the sunny side of Venus will be plentiful and reliable 24/7. It might also be possible to harness wind power with wind energy generation kites or aircraft.
With other potential sites, the energy supply is more challenging. For example, Mars, like Earth, will have nights so energy storage will be required. Mars will also have occasional long-duration dust storms. The Moon has longer nights so a colony there will require a lot more energy storage.
Transportation Infrastructure
Colonies on the Moon or Mars will require transportation infrastructure and vehicles that might not last long because of dust. Aircraft on Venus will be able to travel from place to place without any additional vehicles or roads. It will be relatively easy for colonists to visit each other if their flying habitats are designed to be able to dock with each other while in flight.
Gathering Resources
Nitrogen, Carbon, Oxygen, and Sulfur are abundant in Venus's atmosphere and could be converted into various plastics and carbon composites using energy from the Sun. The concentration of water vapor is only 20 ppm, therefore extracting water from the air and recycling it may be more of a challenge. Possibly a side mission could divert a small comet to Venus to increase the concentration of water in Venus's atmosphere.
Other minerals can be mined from mountain tops such as Skadi Mons, the tallest mountain on Venus, which rises to an altitude of 11,520 m. At this altitude, the temperature is 377.45 °C, which might be just cool enough for robots equipped with airconditioned computers. Such robots could be remotely operated by workers in the flying habitats.
With the elements and minerals extracted from mountaintops and the atmosphere, it should be possible to manufacture all of the parts needed to maintain the existing fleet of flying habitats as well as create new ones. Possibly it will be necessary to provide a very large initial supply of microprocessors, FPGAs, and similar components to ensure that the colony will be able to last for a long time without the support of advanced industries on Earth.
Long-Term Outlook
We could imagine that the population might double every N years. As everyone is living within a three-dimensional space within the atmosphere, the population will only be forced to stop growing when access to sunlight and wind power becomes the limiting factor. At this point, the population could be as high as...
$$Pop=4 \pi r^2 t/(8\rho) = 4 \pi (6,051,800m)^2(4000m)/((8)1000000) = 230,117,158,339$$
Where
$r$ is the radius of Venus
$t$ is the thickness of the populated portion of the atmosphere
$1/8^{th}$ is the fraction of the planet that is populated
$\rho$ is the volume of space per person
With a seed population of 100 people, and a doubling rate of 30 years, the population could reach this energy and space-constrained limit within as little as 1000 years.
With its ability to sustain population growth over the long term, Venus would be the best bet for ensuring that intelligent life survives after an extinction-level event on Earth.