While government fees are set, attorney fees could vary widely depending on a number of factors. Please work with a counsel to get a reasonable range of numbers.
The foregoing does not constitute legal advice. No attorney-client relationship exists between me and you. Please consult a qualified attorney before making any significant decision.
You need to work with intellectual property counsel. The appearance of a website will almost certainly NOT qualify for design patent protection. Far more important will be copyright and/or patent protection for the software that runs the "unique features" of the website and copyright and trade dress protection for the appearance of the website.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
What you would be applying for on the patent side is a utility patent directed to the implementation of the unique features, not a design patent which covers the aesthetic features of a functional article. The New York area rates, like everywhere else, vary by complexity and amount of work required. Based strictly on hourly billing rates, rates on Long Island and in New Jersey at smaller firms will be less than Manhattan or ":big firm" rates.
In general, in my experience, patents for software-related functionality run from about $8,000 and up. The only way to know is meet with a patent attorney to discuss the particular invention.
This information is intended to be general and educational in nature. It is not intended to be specific legal advice or establish an attorney-client relationship. I require a signed retainer agreement from a potential client to establish an attorney-client relationship and before I will provide specific legal representation.
I suggest that you may not be asking the right question. What it seems that you seek is to develop an efficient strategy to generate the maximum rights to the intellectual property inherent in your website. Development of that strategy could start with an intellectual property audit of your project, examining the contracts you have with your colleagues developing the site, the possibility of registering copyright in both the "look" of the site and the underlying computer code, the possibility of registering one or more trademarks to protect your business names and Internet domain names, and then perhaps the possibility of obtaining patent(s) for inventive subject matter.
It's less likely that a U.S. Design Patent would be pertinent to a new website, though design patents have been obtained for some unique icons.
Also beware that a U.S. patent cannot lawfully be obtained to protect an "idea." On March 20th of this year, the Supreme Court reminded us that when a patent claim recites a process that is little more than an expression of a law of nature (itself, an idea) that patent claim is invalid and should not have been issued by the government agency that gives out patents.
As other responses to your question have suggested, it would be worthwhile for you to consult an attorney well versed in intellectual property and then listen carefully to the advice.
This posting is intended for general education and isn't "legal advice." It doesn't create or evidence an attorney-client relationship. You are encouraged to engage an attorney in the pertinent jurisdiction for confidential legal advice on matters of any importance.
You are asking the wrong question---indeed, in the scheme of things this is the least important question you could ask. If you are developing a web-site, then you need to develop from the very beginning a comprehensive strategy for (a) procuring and protecting your intellectual property rights, and (b) assuring that you can operate your web-site (with its allegedly unique features) without violating intellectual property rights held by others. Failure to retain IP counsel to assist you developing such a strategy is almost always a major strategic mistake. Anyone who proposes to operate a web-site will face literally dozens (if not hundreds) of intellectual property and business law issues. It is critically important that you involve intellectual property and corporate counsel from the very beginning of your planning for this web-site. Operating a web-site is a big deal---you are competing with web-site publishers who have millions of dollars at their disposal to lay the proper legal foundation and take aggressive actions against those who might be perceived as a competitive threat. I regularly work with "start-up" web-site companies and inevitably the wizards behind these companies come into my office with the false belief that their legal problems can be explained to them and resolved in a brief one hour consultation. at essentially no cost. This is never true. You need a substantial budget for laying the proper legal foundation to operate your web-site and if you do not have such a budget, and if the first issue that you raise with the lawyers is "patent cost", then you are on the wrong track.