I got a few comments and emails about this, thus this post.
Los Alamos is about 45 minutes north of Santa Fe, so you can drop the ol' ball and chain off at the galleries and drive up (of course, there's also lots of great riding in Santa Fe). It's also close to Taos if you're there for some (probably the same) reason.
Los Alamos has a mountain bike club, the Tuffriders, who do regular weekly rides from Spring-Fall for all ability levels. They tend to stick to their tried and true favorites, and they ride after work, so it's a great way to see the in-town trails, but not so useful for seeing the higher elevation/longer rides.
Trail maintenance is done by the awesome Craig Martin (a fixture of the trails for decades and now the county's pro trail guru) and a mix of paid county employees and volunteers. Craig has a trail conditions blog here. Yes, you can email him and ask him to remove a downed tree - and he will go do it, usually within a day or two!
My favorite rides, listed in no particular order:
-Quemazon to Pipeline to Guaje Ridge to Cabra to Perimeter - probably about 30 miles, basically all singletrack, lots of elevation gain/loss. Get a local to show you where to go!
-Town trails/Perimeter loops. Many combinations possible. Not too much elevation gain, these trails wind through town on the sides of the canyons and finger mesas.
-Nail Trail/Pajarito Canyon. Short but sweet. A nasty climb is rewarded with a rad singletrack in a beautiful canyon. There is great rock climbing (at the Dungeon) here too.
-Cochiti Mesa/Graduation flats loops. A bit of a haul from town if you're riding (though I used to do it quite often) but only 15 minutes in a car. Great network of singletrack, with everything from buff and fast to super techy. Aspens to desert.
-Downhilling at Pajarito Mountain. When I was there, there was only really one trail, but it was darn fun. Now there are a TON, and a chairlift running (we would just ride up back when men were men!) Get your pads on!
Unfortunately, I have not been in Los Alamos in quite a while, and businesses tend to crash and burn frequently there. As far as I know, there is NO BIKE SHOP, and there may or may not be a place to get a beer after your ride. The Trinity Beverage Company used to have some beer, but I'm not sure it still exists. Food options are mediocre except for (if it's open) the best greasy green chile stand ever - Chile Works. Many an hour did I waste their scarfing my favorite veggie green cheese burritos...