My daughter and I called it "treasure hunting" too when we first started. She can usually spot caches before I can, now!
As far as urban/suburban caches, I avoid them as well. Too many people milling about, scenery is, well, urban! Geocaching's main appeal to me is another excuse to get out and about in the boonies.
One of my favorite caching areas abounds with dirt bikers, Jeeps, ATV's, etc. Gotta be discreet approaching a cache there, I don't want to tip anyone off that there might be something there. We usually only go there now during the middle of the week.
Anyway, I am glad you and your kiddo are enjoying it!
P.S. FWIW, I use a plain vanilla Garmin Etrex.
P.P.S. Ed, do you remember the name of the travel bug?