2003 Honda Accord A/C blowing hot hair

Air Conditioning problem
2003 Honda Accord 6 cyl Front Wheel Drive Automatic

I have a 03 honda accord V6 with 85000 miles and my a/c has recently been blowing hot air. I took it to the dealership because the a/c turns on for a bout 10minutes then all of a sudden it starts to blow hot air. Well they said it could be the A/c clutch and coil. And they were going to charge a good amount to fix it. So my question is, is it cheaper and safer for me to take it to the dealership and let them fix it or look around and see if I can find it cheaper like at a local automotive shop?