In my experience, the "local web design company" should be able to offer font and layout ideas for you; that's part of what they DO. To me, it would seem that your job is to make sure that the content is current and relevant, and that all the information is there. But for ideas, look at other sites for similar places. Are there other eateries in town that have sites? Surf around and do some recon. There's no hard fast rules on any of this.
btw, as far as Facebook and Twittering, also in my experience, if there's no "plan" in place on how you're going to engage your customers/clients, then you're setting yourself up for failure. Too many people think "oh shit, I need a Facebook page!" but they haven't really fleshed out how they're going to engage-- what are the goals? how are you going to measure your success? who's updating the content? how often? One thing I do know for sure, people on Facebook do NOT like to be marketed to, so there needs to be clever ways of engaging your customers.
also: regarding fonts... is there already some sort of "identity" associated with the eatery? Do all their menus, print ads, etc. look the same? You'll want to maintain some consistency online with what you're already doing.
Just my .02.
edit: check out what Naked Pizza did to launch a really successful Twitter campaign.
http://www.squaremartinimedia.com/twitt ... ked-pizza/