So thinks to ask:
First things first: how many hospitals do you have to cover. If the answer is more than one, you probably don't want to do it. If its multiple hospitals but they are very close together, that might be OK. If you have to spend 30 minutes driving between them, pass.
What's specialty coverage at them like? If its a small hospital with no/minimal pulm/CC I'd stay away. You don't want to be missing any major specialists because you either than have to transfer often or just do your best without - neither are ideal.
How big is the group and are any of them over 60. You don't want to go from q4 to q3 6 months in because the 68 year old guy decides to retire.
Do you take overnight call? Lots of places will have the hospitalists admit/manage overnight so you're only responsible for care from like 6a-6-7p M-F and maybe weekend mornings. If you're 24/7, that sucks.
What's the daily schedule like? We have a group that in inpatient until about 10:30am and then clinic. We have another group that each person is basically the office hospitalist every 3rd week.
That's all the stuff specific to a traditional practice I can think of.