Why wouldn't it travel higher or lower?

The reason why the Concorde would not cruise higher is due to Cabin pressurization.

The Concorde flew at around 56'000 feet (Above Sea Level) which when comparing it to your average flight from the same destination (New York to London) with a regular aircraft, it is hugely significant.

The Concorde's pressurization was set to an altitude at the lower end of this range around 6,000 feet. A sudden reduction in cabin pressure is hazardous to all passengers and crew. By the time the passengers and crew would of donned their oxygen masks, hypoxia would of already start to set in. The plastic masks at this altitude would of also been not very useful,

Another reason is because of the engines and the aircraft itself.

The engineers would of set the aircraft would be most effective (fuel consumption wise) at 56'000 feet.