If there's a Premium Crossover category available, book that. You'll almost certainly get an Enclave or an Acadia SLT, both are very nicely appointed, comfortable for 4 people, and get better gas mileage than the Suburban or Tahoe.
The problem is that sometimes locations make these unreservable. I ran into that at TPA last year, had reserved the Premium SUV and all they had were Tahoes with relatively low roof lines. I wanted to change my reservation to Premium Crossover to get the Enclave, and they wouldn't let me - they'd only do it as a $75 paid upgrade for my 5 day rental. They said that if I called the 800#, the agents wouldn't be able to see any inventory for that class and wouldn't be able to change it.
Needless to say, i was rather torqued off.