How can I have a live private version of a website to show a client without having to pay anything?

I've been doing personal website projects for a while now. My skills are only in the front-end of things. However, I have had an offer to create 2 satellite websites and this will be my first commercial website job.

As excited as I am about this there are a few things that have thrown me already that I feel I should've been prepared for before hand. One of them is the client said "I trust you have somewhere private you can work on the site where we can both see it?". I don't have anything like this. I cannot afford a deluxe hosting package whereby I can just throw up hosting with decent space just like that etc. How do all of you do this? I'm not in a position where I can meet the client very often in person to show them.

How should I go about this? Really need this advice as I am supposed to be acting very professional and I don't want to cause any confusion?