If Ahsoka is to live following the Clone Wars, then one likely scenario would be her leaving the Jedi Order and Republic military before Order 66 is initiated. There are a number of storylines that could play out to explain Ahsoka leaving the Order. Perhaps she falls in love with Lux and they decide to leave the conflict behind and run away together. This one seems far fetched, but Ahsoka’s friendship with Lux certainly exposes her to life and relationships outside of the Jedi Order and opens up this possibility.
Perhaps Ahsoka simply becomes disillusioned with the Republic’s war effort. Does Chancellor Palpatine order Ahsoka to do some particularly heinous act. If she does it perhaps it drives a wedge between her and Anakin, or if she refuses perhaps she is removed from the war effort. Maybe she simply cannot emotionally handle killing any more and leaves the Order and the war for those reasons.
Perhaps Ahsoka leaves the Jedi Order and joins a splinter group such as those Jedi following Master Altis.
What if Master Yoda fears the war is costing the Jedi to many lives and decides to send a select few Jedi far away into the Unknown Regions or another area of the galaxy to hide and keep the Jedi flame lit should the worst case scenario happen, the Separatists win and the Jedi be crushed in the war. Ahsoka, as a young and powerful Jedi who has learned from some of the Order’s greatest modern Jedi could be a logical choice for such a group.