Should the lender tell you where your repossessed car will be sold so you can buy it back?

It is not required. However, if you do discover where the vehicle is to be sold, provided it is close enough for you to travel, you can attend if it is a public auction as opposed to a dealer aution, and you bid like everyone else.

Now, that being said, it seems it would be much easier for you to pay the redemption and storage fees, reclaim your vehicle, and get out for less than if you were to attempt to purchase the vehicle. You will be help accountable for the fees regardless, and the money you pay goes to the lender either way.