I second Robert M.
The process is costly due to the equipment they use. You may also do it yourself, but will take you up to four hours because you have to drain and fill between reaching operating temperature (thermostat open; 180*-195*). Unfortunately it's a necessary evil.
Take it to a shop for a cooling system pressure test before you change / flush it, if the car is overheating you will be wasting your money when they drain it out again to repair it. If it passes the pressure test, tell them to flush it. I'll bet they will find a leak. Don't mention the coolant flush until you get a good pressure test. No year/model info, many cars are easy to flush if they don't have that stupid European style recovery tank setup.
Dupage tire has a 4.7 star rating for cooling system repair in your area - http://www.dupagetire.com/
$150 is NOT ridiculous. That's actually a fair price. Plus, they'll use the correct coolant instead of a universal coolant. I wouldn't trust any of the oil change places to put air in my tires, let alone do a coolant flush.
You can do the flush yourself. Go to Walmart and get a flush and fill kit. The antifreeze brand does not matter. All are the same ethylene compound. Car manufacturers do not make their antifreeze, they just buy it from one of the antifreeze manufacturers and put their label on it. The only difference between antifreeze is whether it is green/blue or pink/orange. Green/blue is standard antifreeze and pink/orange is extended use. Incidentally, you can intermix them. Flushing the radiator at a service facility should only cost about $60 to $70 and can be done by anyone with the slightest mechanical ability.
DO NOT TRUST ANY OIL CHANGE CENTER WITH THIS JOB! they use INFERIOR parts, and FLUIDS usually! $150 is NOT a bad price if you get a full WARRANTY on the work! There are at least TWENTY different coolants out there, and it is CRITICAL that you get the right one! Gm was SUED BIG TIME over DEXCOOL and it's tendency to eat up GM chosen gaskets and plastics affecting nearly ALL cars made from 1996-2005! If this is a VW, use VW coolant! if this is a HONDA< use HONDA coolant, ETC! EXCEPT for GM cars! DO NOT USE PRESTONE because NO factory uses it! NO factory uses VALVOLiNE EITHER< and it makes many engines CLOG UP WITH SLUDGE and TAR! ALl fluids these days are VERY FOCUSED on specific models! THERE ARE NO UNIVERSAL FLUIDS for ANY car! NAME year, make, model engine size,m country of origin ,and MORE with your AUTO questions! DIFFERENT ANSWERS for each one! GO TO DEALERSHIPS where they give a WARRANTY on the work! When I use JIFFY LUBE< I bring my OWN fluids and filters because I know what works and what does NOT work! GOOD LUCK!
Use yelp.com and find a highly rated independent automotive center in your area.
The dealer is riduculous and wants $150 for it, Jiffy Lube I'm not so sure I can trust. So where is good for a flush? I'm in Schaumburg IL