It's more than your budget, but I'm still amazed by my Fenix LD01 (AAA, 77 lumens on high). I was at a Cub Scout event a couple weekends ago and we needed to light a stage with flashlights. My little EDC keychain light out-threw almost every other light I saw and it kept running through the whole program.

I originally carried an Arc AAA-P which is about 10 lumens. While it was enough light in most circumstances, I switched to the higher-powered Fenix after I had to go from bright sunlight into an almost completely dark building. The little Arc wasn't enough for me to see anything and I had to stop and wait until my eyes adjusted to the dark. The brighter Fenix doesn't have that problem.

I can still use it on a lower power setting if I want to, but the bright light is available if I need it. I think the default is 28 lumens, one twist takes it to 3 lumens, then a second twist takes it to 77 lumens.