My radiator fans have recently quit working. I look through my fuses and they seem to be fine. Where would a good place be to start trouble shooting this?

check to see if the fans are getting any voltage? the motors could have died. also look for any burned wiring.

I don't recall if the 97 had fan relays. Check a repair manual and if so you may want to take a look at them / it.

I had the same problem, my 20 amp fuse under the hood was shot but you could not tell by looking at it, had to take a meter to it. Do that then check the relays if you have them, if they are good jack the car up and take two jumper wires and connect them to then hook up on the fan motor one wire is black for negative so keep track of what wire is on the negative for when you hook them to power), get above the car and touch the jumper wires (hold them by the wire NOT the metal leads) to the battery, if the motors are good the fand will run at full bore. Don't connect them to the battery then let them hang as you get under the car because the leds could touch or something. If the motors, relays, and fuse is ok it could be a problem in one of the sensors and as far as I know you need a scan tool to make sure the computer is getting the signal the the engine is at fan temps.

go here for some more info http://shbox.com/1/4th_gen_tech2.html#radflush and go down to Cooling System Operation and Testing

Do the fans come on when the a/c is turned on?

You can test most of the system by finding connector C100 on the RH shock tower. It will be similar to the pic on your 1997. Unplug it and use a test ground lead to touch the green and blue wires on the side of the connector toward the front of the car.
Touching only the green wire should operate both fans at low speed.
Touching both green and blue at the same time will operate both fans at high speed.
Touching only the blue wire will operate only the RH fan at high speed.
If all that works, there is no problem with the relays, fans, or wiring from that point forward.
This is basically doing the same thing a manual fan switch does.

On the 1996-1997s, you don't need the key ON to do the above tests. On 1995 and earlier, you do. There are also some differences with the fans in 1993-early 1994. You can read about that on my Tech Page.

Let us know what it is doing.

I did what shoebox suggested and the fans do come on when using a test lead at that point. What do I start to look for now?

Check the temperature sensor on the water pump.

what do I check it for? I looked and it is hooked up

You tested at C100, right? Try this-at the DLC under the dash, short pins 5 and 6 together. Turn the key to ON. The fans should run at high speed. If they do, the PCM is capable of turning them on. Most of this testing info is on my Tech Page.

Check the sensor itself, it could be bad. If you have a friend with a same car you can switch and see. If not you can check the voltage output of the sensor, I think shoebox has the voltage versus temp table on his page.
I,ve seen this sensor causing fans not to operate on a couple of camaros at my friends shop.