Define "Jobs that don't need to be done". As Capitalism is ruthlessly profit-seeking, every job currently in place in free markets provides value to somebody. There are some in non-free markets, but that isn't affected by UBI existing.
A possible example would be many cast food positions. If the workers didn't have to work together by wages would go up driving up the cost of fast-food. The higher cost would lower demand, and it might not make sense to have 10 fast food restaurants on every block.
But now we're back to one of the key criticisms of UBI - reduced labor supply leads to higher wages but reduced employment, increased prices, reduced economic activity and consequently decreased consumer surplus (which would be a bad thing).
In either case, I don't see anything special about these jobs that would make them the first to disappear in the face of UBI.