One of the first places where rare uranium is found is the planet Remav or H-047C. This is one of the "golden worlds" discovered by the Andromeda Initiative. Players can visit this planet after they interrogate VehnTerev in the fourth story mission, Hunting the Archon.
Travel to the planet and exit the ship. Use the Nomad and travel southeast of the Tempest landing zone. You need to get to the huge dome. There are several uranium nodes here that should help you collect several hundred material.
Also, uranium can be obtained during the fifth story mission "Journey to Meridian" (Journey to Meridian). Several uranium nodes will be in Hitashira, which players can reach after they have landed in the Relic City in the Tsivki system.