1997 Buick Skylark is leaking coolant from a valve on the firewall, which appears to be next to one of the AC lines. Any ideas?

because it needs charging there is a leak in the system
Don't waste your money filling a leaking system
Have an accredited ac specialist shop fin/fix the leak and recharge the correct amount.

first you must determine if you have r12 or r134a to find out find the compressor follow the 2 hoses on should go tward the radiator and one should be heading back tward the firewall. you should find a valve on each line. now to determine which coolant r12 will have a small valve that looks like the valve on a bicycle tire. r134a will have a bigger valve that has a ring around it as to accept a snap clip. your local parts store should be able to show you the difference. if you have r12 then my suggestion would be to have a shop do the retrofit for you for around 100/150 dollars. hope this helps

Sounds like a water pump ...cost around $100.00 parts and labor..

FOLLOW AC COMPRESSOR SUCTION SIDE FROM THE ACCUMULATOR CANISTER TO THE SMALL EVAPORATOR LINE GOING INTO FIREWALL LOOK FOR LINE WITH A BLUE PLASTIC CAP.THATS YOUR LOW PRESSURE CHARGE PORT.

tje heater core is leaking in the dash, be prepared its a time consuming job

the low preasure valve is located on the line coming off the ac compressor, if you look down from the front at the compressor and follow the top line out about 4 inches you will see it, good luck.

VALVE TIMING OR IGNITION TIMING OFF YOU ALSO COULD HAVE A INTAKE MANIFOLD VACUUM LEAK.MAKE SURE YOU DID ADJUST VALVE LASH.

I would like to encourage you to consider buying the service manual for your car; they can answer questions such as your current one and help you decide if an estimate you have gotten appears to be fair or not.
Buick Skylark manual

follow lines from firewall or compressor and the larger diameter hose & piping is usually low side. Look for shrader valve on it with cap over it.

Did you replace the schrader valves (the thing in the inside of the A/C service fittings, you need a special tool to remove and install them) before you recharged the system? They are notorious for leaking if they are old.

If you did not, replace those and try again, if it leaks out again with no evidence you most likely have a bad evap core.

And yes, it's a pain in the ****, plan on it taking a 30 pack of bud light and a weekend to do, or one day and a 12 pack if you are good. Just start taking the dash apart, and may the force be with you. It will be behind the glove box