It really depends on the make of the car. I am in the process of buying a used Jetta so I took it to a German Car Specialist.
If the car if relatively new, take it to the dealer. If you are buying a Ford take it to the Ford Dealer.
For older cars just look for a good quality shop that does general repairs. If you don't know a mechanic or don't have a friend, relative, co-worker or neighbor who can recommend a mechanic just look in the phone book, call them up, ask them if they do used car pre-purchase inspections and make sure they are ASE certified.
This job should take about 1 to 1 1/2 hours and cost between $60 and $150 depending on the make of the car and how thorough the inspection process is.