Out of state llc?

I live in New York city and operate a business that earns me exactly zero dollars. It is a free service, to help people cook. The majority of it happens on the internet.
I am in the process of making everything official in hopes of eventually turning a profit. I have limited funds, and was going to make it an llc.
In New York the cost is around $650, plus more in potential publishing costs. In Georgia however, I can do it for $100. A significant difference for a business with no profit.
Since most of the business is online, is there a reason I shouldn't file for the LLC down in Georgia, and operate remotely as opposed to eating the cost of the NY llc?
what are the pros and cons of my options?

What makes you think you need an LLC at all?

why I think I need an llc?

Mainly for my own liability protection.
I provide free cooking advice, If if someone misinterpreted my advice (or I gave bad advice) and got sick or died, my company would be liable. (not me personally)

This is my impression. Please correct me if I'm wrong.

Also the concept is growing quickly and I'd like to have an entity under which to conduct any possible business that comes my way.
I'm also a working chef, and could eventually conduct my private work (small scale catering) within the llc.

New York law requires that an LLC name contain the words "Limited Liability Company" or the abbreviation "L.L.C." or "LLC". Additionally, your business name must be distinguishable from other names on file with the Department of State. There are a large number of words that cannot be included in the name without prior approval. For a full list, see N.Y. Ltd. Liab. Co. Law § 204 (link is to entire code, you need to click on the LLC section, then choose Article 2 and locate the specific provision).

There are also state-to-state differences in how LLCs must be run/operated on a day to day basis. Failure to follow those rules, whichever they may be, could very well result in the loss of your limited liability protections. In other words, which state has the least onerous requirements?

There are also the potential tax consequences to consider, if there is/will be any money involved.

Needless to say, there are plenty of other considerations on which state to file in which go beyond a simple internet forum.

Good luck, though.