I had a similar situation recently with our 05 RX330 - a young girl backed into us in a parking lot. It was clearly her fault but no witnesses, and no police involvement because there was no personal injury and no jurisdiction in parking lots. Fortunately, her own insurance (Geico) caught her lying and assessed it as 100% (her) fault.
The claims adjuster gave us checks for the repairs and rental, and sold their own shop as "the best". They didn't do a very good job of explaining why they were "best" so I called my Lexus dealer. They have a nearby bodyshop do all of their work, and said that all they do is Lexus bodywork. I ended up taking it there, and they did a fantastic job. The rear bumper and one lens was damaged, and you simply cannot see any evidence of it anymore.
In my case, cost was the same regardless of where I took the vehicle for repairs. With this kind of vehicle, plus the fact that it's new, I wanted the best job possible done on it. Repairs came to just under $700.
I hope your repairs were done (or will be done) as well as mine. Good luck!