We don't know the composition of the asteroids or the objects in the Oort comet cloud or the Kuiper belt in great detail. One theory of solar system formation is that there are more metals in the inner solar system. That would mean most of the uranium is Mars, Mercury, Earth Venus and asteroid belt. There is an estimated 40 trillion tons of Uranium and 120 trillion tons of thorium in the Earth's crust. Most of that Uranium is concentrated in the continental crust. The mantel has lower concentration of uranium, but there is a lot more mantel and mantel recycles out to crust.
The solar heavy-element abundances described above are typically measured both using spectroscopy of the Sun's photosphere and by measuring abundances in meteorites that have never been heated to melting temperatures. These meteorites are thought to retain the composition of the protostellar Sun and thus not affected by settling of heavy elements. The two methods generally agree well.
Meteors tend to only have 0.008 ppm uranium
The Sun is 332,830 earth masses. So if the Sun was 8 ppb (parts per billion) uranium, then 0.27% of an earth mass of uranium in the Sun.
The National Physics laboratory (UK) has an estimate of the amount of all elements in the sun, solar system, meteorites, crust and ocean
0.018 atoms of uranium out of every 30 billion atoms in the solar system. 1 out of 5 billion by weight (1/40th of the meteor estimate). Then about 0.005% of an earth mass of Uranium.
99.8% of the total mass of the Solar System is the Sun. So the Uranium that is not in the Sun in the solar system is 500 times less than 0.005% of an earth mass [1/ten millionth of an earth mass]. One earth mass is 5.9742 × 10^21 tons. So 6 x 10^14 tons of Uranium. An estimate of 600 trillion tons or 12 times the amount in the earth's crust for Uranium not in the Sun in the solar system.
There definitely is a lot of metal (iron, platinum) in the asteroids.
One NASA report estimates that the mineral wealth of the asteroids in the asteroid belt might exceed $100 billion for each of the six billion people on Earth. John S. Lewis, author of the space mining book Mining the Sky, has said that an asteroid with a diameter of one kilometer would have a mass of about two billion tons. There are perhaps one million asteroids of this size in the solar system. One of these asteroids, according to Lewis, would contain 30 million tons of nickel, 1.5 million tons of metal cobalt and 7,500 tons of platinum. The platinum alone would have a value of more than $150 billion.
The outer Oort cloud is believed to contain several trillion individual comet nuclei larger than approximately 1.3 km (about 500 billion with absolute magnitudes brighter than 10.9), with neighboring comets typically tens of millions of kilometres apart. Its total mass is not known with certainty, but, assuming that Halley's comet is a suitable prototype for all comets within the outer Oort cloud, the estimated combined mass is 3 × 10^25 kilograms, or roughly five times the mass of the Earth.
Models predict that the inner cloud should have tens or hundreds of times as many cometary nuclei as the outer halo; it is seen as a possible source of new comets to resupply the relatively tenuous outer cloud as the latter's numbers are gradually depleted
The collective mass of the Kuiper belt is relatively low. The upper limit to the total mass is estimated at roughly a tenth the mass of the Earth, with some estimates placing it at a thirtieth an Earth mass.
There is uranium and thorium on Mars
There is uranium on the moon.
Several of the larger moons in the solar system and planets could have substantial percentages of uranium in their cores. There is a controversial theory that there is a lot of Uranium in planetary cores. Some spectral analysis of the surface of some solar bodies a couple of sampling missions and guesses at what is in the core of objects is what we are going on.
A discussion of uranium in the solar system