Does anyone have a Garmin Edge bike computer? How well does the GPS work on the local and regional trails like the GAP and the C&O?
It depends on the maps you have loaded. I suspect either the Garmin maps or the ones you can get for free from http://garmin.openstreetmap.nl/
would work quite well. But I'm not completely sure because I just use it for navigation and turn it off when I'm on the trails, to save on the battery.
Can you define what you want to work on those trails?
For the most part they perform well. You'll lose some resolution under heavy tree cover or anything else that blocks line of sight. The 1000 and the 520 are a bit better in that regard. But it's an after the fact sort of thing (eg the track on Strava may show you parallel to the trail by 3 meters or something)
I guess making sure I know where I am, how far to the nearest town. I don't need super precise estimate of what the path looks like. (Ie, don't care if path curves in 200 feet)
It'll work well for that. You can get distance and speed reliably. If you need more reliable you can always buy sensors.
The 500 doesn't have mapping really. It'll show you a breadcrumb trail but not roads and such. I'm not sure about the 510 in that regard. The 520 does have this and the open source maps are quite nice.
I have a garmin edge touring and it works well on the C&O/GAP. I was pleasantly surprised that all the trails at Acadia National Park were on the map. Best thing you can do is to keep the maps up to date. Also, turn off auto-rerouting if you use it to follow a route. This keeps the map from changing if you decide to take a side trip. You'll likely want it tell you you are off course rather than change the route. I bring an external usb battery bank for long trips, just in case I have a really long day.
This is a very helpful link for the edge series: http://www.dcrainmaker.com/2013/05/download-garmin-705800810.html