My experience says that 6000 feet will be noticeable, but you'll be able to, say, climb a flight of stairs and be a bit more winded than usual. As another example, the Paradise visitor's center at Mount Rainier sits at (IIRC) 7K feet. Plenty of fat people waddle out of their cars and make it across the parking lot just fine. They don't generally go very far up the mountain, but they make it. And the residents of Denver, CO seem to survive at 5200 feet.

To me, "noticing altitude" starts at about 10K feet. For reference, life-long endurance athlete who still stays in pretty good shape in his middle-age.