Hi,
Is it OK and safe to run a wire from the panel up to a junction box in the attic that runs wires to two rooms on one side of the house and then run a wire from that junction box to another junction box on the other side of the attic and power another room from that box?

Basically,
Is it OK to run from one juction box to another and have wires come out of both to power rooms?

Thanks,

Yes it is OK to do, but why? Just run from box to box, room to room.
Why bother with j-boxes at all?

It is OK to have a junction box in an accessible location in the attic. What you have to take in consideration is the load that will be on the total circuit for each room. You may want to run a single 3 wire with ground (red, black, white & green wires) from the panel box to the attic and run each room off a separate breaker. Room 1 can can use the red and white wires. Room 2 can use the black and the same common white wire. The green wire is the ground.

In the panel box the red wire would connect to circuit breaker to feed room 1. The black wire would connect to a separate circuit breaker to feed room 2. The white and green wires connect to the ground bar. Size of breaker and wire to be determined by load on circuits.