Hire a small plane to drag a banner in the sky over beaches, other large crowds, etc., with your url on it. Sponsor a sports team and have your url on a sign in the arena or on the team's uniforms. If your budget does not allow for such mass communications, how about approaching the business editor of your local newspaper and seeing if you can come up with a news story about your business that would be of interest to the paper's readers. Note that the key word in the previous statement is "news". You must have an angle that the editor and his/her readers will find interesting and topical, and not just an announcement about your website.
There is an easier way. I purchased the PR Model tinfoil hat. You simply place it on your head and it somehow transmits sonic PR vibes to potential clients around the world, works great. The only downside is that you may get some stares, and some people might laugh at you while you are driving around with the hat on.
If the site is hyper-local there can be value in off line. I'm wondering if the OP meant off-page tho.
Banners, promo materials that would be handed out in person in some store or in some open space, some radio or newspaper ads, and so on. But, if you are promoting a website, I would say that online promotions are always a better option as you can measure results and everything and I don't really see what could you achieve with the offline presentation, but you can give it a go.
I would like to suggest a few things where you will be able to promote your website offline. 1) Ads in the newspaper. This way, you will be able to do good marketing. 2) You should organise a public event and should call to the public. After that event, you can tell the public about your website. 3) You should go door to door in houses and tell people about your website. Then they will know. 4) You also need to make a business card. After that, you have to provide a business card to every person who meets you. In this way, you can also promote your website through business. 5) You should also enlist the assistance of family and friends in spreading the word about your website, as this will provide you with good offline promotion.