Definitely 2nd CarMax -- they make it painless, however for new, they only sell a couple brands. For used, the only way to do better is person-to-person sale. I went back there for my current car, a 2012 Mazda3. I had very specific requirements, and the one car that met all of those requirements was in New York, and they shipped it to my local dealer (not for free, mind you, and with 2 weeks of shipping time, roughly).
For new, TrueCar buying service or similar is the way to go. Here's how to work them: do some research, find out which dealers in your area are good and which aren't. Then determine which car you want, then go to TrueCar, enter the car, option it out the way you want. They'll come back with some in your area -- they may not be an exact match, so check carefully.
Now the way it's supposed to work, you should get calls from several dealers, you pick one, and you go with them. But the way my friend worked the system, he took the lowest offer to the dealer he really wanted to go with, and they beat even that price.
As usual, make sure they don't stiff you on the trade-in, financing, or any other areas. Try to make sure that you are in the position of always being able to walk away.
Last thought: it still might be worth it to get it fixed -- tdiclub might be able to find you a good, honest mechanic in your area even if it's not a TDI (they're all VW fanboys, so it's a good network for that). I know I have one really close to me in Woodbridge if I were to have gone that route.