Question

what truly acceptable solutions have we found for storing nuclear waste?
none, yet
shooting it to the sun

Explanation:

Shooting nuclear waste to the sun is unfeasible due to extreme cost, high risk of launch failures that would spread radioactive material, and technical barriers. To date, no fully globally accepted, permanent, large-scale solution for nuclear waste storage has been implemented, with only temporary storage and experimental long-term concepts (like deep geological repositories) in development or limited use.

Answer:

none, yet