Yes you can live at (near) any of the listed gateways, the choice is yours.
Do not get confused between a gateway and a base, netjets does not have bases. On day 1 of tour the company will position you to where ever the aircraft is. Your colleague, who will almost certainly be "gatewayed" somewhere else, will do likewise. You meet at the aircraft and off you go for 6 days. On day 6 the company will position you back to your gateway, you do whatever you do for 5 days and then start again.
Where you're "gateway" is has no effect on the number of hours you fly, different fleets tend to have different types of flight. Each type has its own challenges, some may fly less hours but that can mean lots of short busy sectors, others have longer sectors but have the fun value of dealing with eastern european air traffic, the GV guys just have it easy
