Are you tightening the knurled nut on the valve so it's closed tightly by hand after inflating? Odd that a new tube would leak after a few days. I second the inspection of your existing tire. I've found things like thorns in my tire.
I got a flat on the trail last night from what appeared to be a 1/2" of some kinda animal quill... that one was hard to miss inside my tire along with the 10" long puddle of slime in my tire.
Side tip - buy a container of baby powder and throw it into your bike tool box. When changing tubes, I always make sure the inside of the tire and the tube itself have a good dusting of baby powder. Helps against pinch flats since the tube can slide around the inside of the tire a little.