Either a Yamaha WR250R, or a 98-99 Suzuki DR350S will make you happy and do what you're asking for.
My wife loves her DR (441 kit/pumper carb/2" lowered)...it's her second one. She recently bought a 2012 Husky TE250 Low (factory lowered 2") and loves it, but we dual sport locally. There is no way this thing can do the long miles to/from the riding area as you describe...really need a wide ratio transmission for that.
"turn it on man, turn it on-whatever, whoever you are-TURN THE FAWKER ON!" -Herbert Foster Gunnison