Carmax is a ripoff in my opinion.
Call your bank's loan department and ask them for the 'black book' values of the year, make, and model vehicle you're looking for.
Your looking for the following numbers:
Loan value
Average wholesale (or trade-in)
Retail Average
Retail Clean
You should pay somewhere between the average wholesale and the retail value of the car.
Carmax will always hit you on the high end and it could cost you and extra $500 to $1000. On the flip side of that they are about the fairest out there in terms of your trade-in but even then you will never get more than wholesale regardless what they tell you (most used car dealers start $500 to $1000 below that number!!)
Check out
www.carbuyingtips.com
To answer your original question, I don't think it matters where you buy the car from (carmax, dealer, private party) just know what the car is worth before getting into negotiations and stand your ground if you know your numbers are right.
And see my sig below if you're in the Chicago area!!
Good luck!