I think you would be surprised where you can find gold in New Mexico. I've found gold in my driveway, and I've found gold in the pile of dirt left over after they installed my
septic tank.
Personally, I'd skip the river and pull some dirt(sand) out of some washes or drainage ditches. Just for fun, I'd also try sweeping up some of the stuff on the side of the road
that has washed down from the hills.
You may not have a ton of gold in ABQ, but I can guarantee you have some.. There are gold producing areas around there.
There is a prospecting club in ABQ, I know nothing about them, except I've run across their web site a few times.
First and Oldest Recreational Prospecting Club - Gold Prospectors Association of New Mexico
It might be worth your while to contact them, they do have meetings every month, and I'm quite sure some old timers would gladly offer
a ride to a 14 year old kid that is willing to shovel... I know I would. (with your parents knowledge of course), I wish I had my 14 year old energy and
stamina back.
Remember, gold is where you find it.. I've found it in places that its not supposed to be. Granted not a lot, but it only takes a little bit of shiny stuff to make me happy.
Good luck.