My 2012 Tundra got rear-ended, pushed the back bumper down and dented in the tailgate. The guy's insurance company estimates it's $1300 and wants to cut the check, but I of course need to get it looked at prior to accepting the money.

Where would be a good place to go?

Ella Paint and Body off Tamina (Magnolia) is excellent.

We used 1488 Collision a few years back and they did my truck right. It was about $28,000 worth of damage and they did a great job.

That's going to be a starting point, once vehicle goes to the shop anything else they need they'll get with insurance for a supplement to address additional items. You'll be wasting your time getting quotes from body shops. You can go to 5 different shops and they'll all be different. Find a body shop you trust, set up appt and give them estimate and let insurance and body shop figure out rest.