A newspaper in my area has a weekly section of new websites and sometimes even interviews the people with the big idea. I therefore think Newspapers..especially the ones that are locally published or even magazines may be a good way of promoting your site as they too are looking for new things to publish.
Contacting a publisher may be a good idea...

I've been surprised at how many times I've seen websites profiled on local news segments. At the time, I thought that it may have been a sign that one form of media's in a bit of trouble, when it starts reporting on another one.

But I think that's a good idea.

you are right there...but I guess...it is one way of being with the times...even the newspapers have gone online now...

our local paper has a small column every week showcasing an interesting website offering a service or products...

It is very effective, and trying to get your pages featured can bear good results.

I think newspapers are still read by so many people everyday...and they can all be looked upon as potential visitors to your site...so the reach is immense if you can tap this resource...

Here in London there is a network of free papers that each cover their local area, these are delivered to homes in the catchement area. A circulation of 159-200k each.. As they are free, everyone will have at least a browse through before recycling them, and they are often useful for local news of upcoming events as well as properties for sale in the area etc.

Getting your site featured, or even just advertising it in one of them can net you some new traffic..