My water bill the past 2 months has been through the roof - we have separate digital indoor/outdoor meters, so I know it's the outdoor usage that is the problem.

I was inspecting the meter this morning and noticed that even with the irrigation system turned off, the meter was slowly ticking up. I also have an area in my grass that is extremely soaked (I stupidly thought the problem was because I was watering the grass too much). If I turn off the valve that goes to the irrigation boxes, the problem stops. And looking inside the boxes, there is not visible leak at those valves.

Considering where the area is wet, the issue could potentially be 1 of the drip lines and 1 of the sprinkler lines. And that's about as much as I know about troubleshooting the problem. ;-)

What do I do from here?

 

First is to find out which zone is leaking. Your problem sounds like one of the valves is leaking to the sprinkler. If a drip zone the drip heads will be wet, If a sprinkler zone a large area or the first or last may be the wettest. This will tell you zone the valve is on. Most valves are rebuild-able. You jest take the screws out and top lifts off replace parts. Parts are Lowes, HD hardware store or irrigation stores.
Be sure to shut off main before rebuilding.

 

Your problem is a broken feed line to a zone box. Dig up the wet area to expose the feed line. With the water valve on, the leak should be easy to spot. Repair parts for the feed line are available.

 

I'm not sure if the feed line is the issue here. The run from the water meter/valve to the zone box is approximately 10 feet - goes from the basement right outside the house where the box is. No water leakage there.

Thinking I am going to have to do some troubleshooting with the valves to try and address the problem. Yee haw.

 

Then the problem is in between the meter and the box.

It cannot be anything beyond the valves because you said when the system is off......
the meter is still registering water usage.

 

Leaking valve to the zone could cause the same thing. Not shutting off when valve closed.

 

If there is a leaking zone valve, all the areas around the sprinkler heads will be wet for that zone, not just 1 area.