If you got the money you can fly directly into Shark Bay, stay at Monkey Mia and see the dolphins. Check. However, the dolphins are the worst part of Shark Bay and only keeps mainstream tourists coming. Most of Shark Bay is hard to get to though, with off-limit islands and a strictly protected marine park. So it's not easy to appreciate this area. You can go to the lovely heritage museum for tons of info on the area: why it's UNESCO, what kind of unique things there are to see, and there is also a small cinema to watch a movie but I didn't stick around for that. I was also the only person in the museum the entire so I guess this place isn't so popular around non-holiday periods.
I actually drove up from Perth and combined this with several sites on the coast, including Ningaloo Coast further up north. I remember trying to fly to Exmouth and drive form there but the mileages was so limited, not unusual for smaller town rentals around Australia including Darwin, that it wasn't going to work out. The drive up from Perth is quite long.
As I was purposely avoiding the dolphin encounter I had to do with just stopping at the coast sites and look around. No mammals or birds in sight. My rating for the site is thus a little lower than it probably is worth because on paper this place sounds great, with tons of animals in the bay. While there is scuba diving it is very expensive and I was already going to go diving at Ningaloo shortly after so I made the choice to do the latter for a lot less $$$.