I was in a very similar situation a few months ago. I ran a URL shortener and got tired of the upkeep, but more importantly, I realized that it's a not product but a feature. I sold it, eventually. Here is how.
I blogged saying the site is going to shut down, and I started making plans about what would happen in terms of data export and keeping the URLs working. The community responded VERY loudly: we like it, don't shut it down, at least give it back to us or sell it. This told me something very important that I didn't realize: no matter how fed up you are, no matter if you hate it or like it, there are people out there that value your work. You just don't it yet.
So I wrote up a brief post about the vital stats with vague ballpark figures, and gave an email address for serious bidders to get in touch. A lot did. Some were not serious at all (easy to tell) and some were very professional and clearly serious about wanting the site. In the end more than one bid was on the table from people that not only wanted the site, but really cared about the users.
How it was valued: an auction. Best bid wins. I kept it anonymous (under the trust that I don't inflate the price, and I never did). If I were to do this again, I would put it up on flippa or sitepoint or ebay or elsewhere.
The biggest problem you'll have is people knowing about the sale. Like anything, market it. Your users are the most likely group to produce the buyer.
The second biggest problem is spurious bids.
And sell everything related to the site. You need to sit down and make a very thorough inventory, and be very careful not to include things you cannot sell (check the licenses) and be sure to include everything you can sell. Included in my sale was a handful of domains, full source code and the whole database.
People will want proof of whatever numbers you give them. Screenshots are OK to a certain extent. Eventually they'll need full access to verify things, like to Google Analytics or your site's admin area. A good way to do this is show them screenshots and agree the sale. Get paid 1/2 or 1/3 upfront, give them access, they verify everything and then you get the rest of the money. Even better, use an escrow service.
Drop me a line if you want more help. Details in my profile.