Hey Amy,
First off, it is awesome that you're thinking about the web presence of your museum as something that can be grant funded. Many people forget that yep, it is one of those things that organizations will pay for or help you pay for.
A colleague and I have been chewing over what makes people to donate to "operations" stuff. It's the old "no one wants to put a nameplate on the loo roll" problem. It is hard to name those things that are less glitzy and special ( instead of a show or gallery or department chair), but still extremely important to existing (toilet paper, light bulbs, roof, website), and it is even harder to find people to fund those things.
Something that I think could be useful, or even just take the edge off of the price tag, would maybe be to work with your development person to court some of the tech savvy people in your city (web development/design firms, engineering firms, etc.) These people may not have millions of dollars to give, but they may have hundreds of dollars to give...and they may eventually morph in to the people who have millions of dollars and can name a building. Maybe set up something like the "Web Circle" level of donorship, or a virtual nameplate type of thing, or something in that vein.
I had a little poke around your site, and it looks like your Society 1858 is kind of in that wheelhouse. I bet those folks have some great networks they could tap to help fund a project like this. Further, there's a great web conference that happens in Columbia called ConvergeSE, and in Charleston there's the awesome Iron Yard...it might be worth cultivating some of those folks as partners? Again, being somewhat tied to the web, you'd be amazed how quickly web folk respond to the call of making a better website.
It is a pretty compelling argument: People visit the website before they come to visit. It is literally the first interaction most visitors have with your institution. If that interaction doesn't work well, it is just as bad as burned out light bulbs, bad signage, or confusing parking. The other argument you can make is because you're currently using Flash on your homepage, which doesn't play well with Apple devices, and mobile is the tidal wave of visitor access, funding for this work needs to be a priority for funding in order to get people there, and to provide equitable access (screen readers don't like Flash either).
What's your ideal launch date for this? You could also consider launching in phases- say you can afford to have your firm do the home page and some other super important bits right now. Get those super important bits live and on the internet. Then while you're rallying for funding, you can pay for other parts to be rolled out.* It is maybe less than ideal, but you can accomplish things and get the big stuff live without having to wait for a whale of a grant to come in?
*That is of course if your contract with the web firm allows for this. It might be worth discussing possibilities for a phased roll out and phased payment system.
Sorry for the wall of text, thinking a lot about websites lately!
Cheers,
Tracey
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Tracey Berg-Fulton
Collections Database Associate
Carnegie Museum of Art
Pittsburgh PA
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