Honestly, I'm not sure that anyone can answer this for you. As a freelance web dev myself, I can barely answer it for myself.
I suggest starting by setting a bare minimum for yourself – the rate you need to charge to survive. Freelancing should probably be about double the rate of full-time employment, as you have a lot of unchargeable (or just plain idle) time, so you have to allow for that.
Then, it's really just a matter of looking around and trying to figure out what other people are earning for similar work. It also helps if you have some idea of the value you're providing for your clients, as your rate should be roughly proportional to that.
For instance, I know one of my main clients charges out (both my time and theirs) at a flat rate of NZ$150/hr, and a bunch of their time is unbilled, so the NZ$80 they pay me is in the "reasonable" zone (especially for pretty solid guarantees of ongoing work). My "survival" base rate would be about NZ$60/hr (NZ$40/hr at the kind of hours I manage to bill wouldn't really provide me a living.)
But like I say, you're in entirely different circumstances to me, so the details don't really translate at all. It's a matter of (for all of us) figuring it out for yourself, really.
My rule of thumb is to set a rate that covers your "survival" if you only had 2 days work per week.
That gives you loads of capacity to try increasing your rate (ie, you won't be desperate for work) as well as holidays etc.
So if you need $40,000/yr to survive, your hourly rate is ($40,000/50 weeks /16 hours) = $50/hour.
Reading the other answers, it sounds like $100/hour is the US market rate. So you have plenty of opportunity to grow from $50 to $100/hour, as quickly as you can. Good luck!
As a former freelancer the lesson I learned from others was to assume you'd spend 1/3 of the year on the bench doing interviewing/conferences/vacation/professional development/searching for the next gig.
So perhaps plan 35-40 hours over 35 weeks. Then set your rate at or above the market rate for your speciality. Don't set it on your cost of living.
If the market rate is too low to live, you'll need a plan on how to upgrade your stature or find a more in-demand speciality.
I guess I'm not suggesting you necessarily have to charge the survival rate, but it's worth knowing the absolute least you could charge and still survive. It's just a "zero" to calibrate your expectations against, so when someone says "that sounds high" you know that it's not actually that silly, compared to your baseline.
Why? I have no idea what the absolute least I need to demand for salary and survive. Why should I? Market rate for my skillset is $100k+ in my area of the country and that's what I calibrate against. If you offer me less than that I simply don't consider working for you.
I suggest starting by setting a bare minimum for yourself – the rate you need to charge to survive. Freelancing should probably be about double the rate of full-time employment, as you have a lot of unchargeable (or just plain idle) time, so you have to allow for that.
Then, it's really just a matter of looking around and trying to figure out what other people are earning for similar work. It also helps if you have some idea of the value you're providing for your clients, as your rate should be roughly proportional to that.
For instance, I know one of my main clients charges out (both my time and theirs) at a flat rate of NZ$150/hr, and a bunch of their time is unbilled, so the NZ$80 they pay me is in the "reasonable" zone (especially for pretty solid guarantees of ongoing work). My "survival" base rate would be about NZ$60/hr (NZ$40/hr at the kind of hours I manage to bill wouldn't really provide me a living.)
But like I say, you're in entirely different circumstances to me, so the details don't really translate at all. It's a matter of (for all of us) figuring it out for yourself, really.