The first thing you need to do before asking any question is to understand the business. So, in other words, your first question should be, can I take a look at your business from A to Z, from the moment the client reserves till the moment he leaves, and everything in between. Take as many notes as you can, ask question to better understand the business, you won't regret this. Be granular: for example, ask how does the client reserve (is it online, over the phone), how does the client pay (credit card, cash), is there a cancellation policy, etc...
Once you understand the business, you have take a look at the logistics of the business, how are the departments connected, how does the internet work, who has authority over who, what are the different levels of access to the network, etc... How does procurement work?
Once you've done this, your second question to the client should be "what do you want from this system?". He will first give you a generic and vague vision of what he wants. Try to get as much details as possible, based on your knowledge that you have gathered in the previous steps.
Now once you've done this, you should go back to your office and formulate all the requirement you have into a readable document, and then check what other similar projects may have. I'm sure you're not the first person developing an Information System for a hotel. Check what has been done before (talk to experts, research on the Internet), compare that to the requirements you've already gathered, and then formulate another document containing the requirements that you think the client will want (including those he already asked for). This is important to avoid scope creep.
Now get back to the client, and start asking him questions based on the new requirements that you have ("do you need this?", "how will you cope without this feature?", "do you really want this feature?", "what do you think about doing this?"). At this point your job is to suggest to the client what he really needs (trust me, most clients have a very vague vision of their requirements), and not let him improvise new requirements, otherwise, you will almost certainly run into scope creep.