Or you can try to find a secular "minister" in your area if the local UU is too religious for you (the amount of "religion" in UU churches varies greatly depending on the community it is in, I have found). You can simply go with Justice of the Peace if you want it done for the legal purposes and then just have a nice secular bash afterward if you want the party aspect still.
My wife and I were married by our old high school English teacher who was also an ordained minister (of the ULC, which is an online ordination set up to get around having to belong to a church with dogma and all of the rest of the crap that goes with it just to be ordained. He got ordained specifically to be able to perform weddings for former students. We not only wrote our own vows, but most of our own ceremony. We stole from Scottish tradition, omitted any reference to god or anything supernatural, had some poetry readings about love and commitment, and ended it off with a very good friend of mine jumping up to yell "Now let's get pissed!" and proceeded to do so with copious amounts of fun, laughter, music and alcohol. We had our first dance, threw garters (I was wearing one too, since I was in a kilt, and it was hilarious!), threw the bouquet, etc.
Basically we kept what we wanted and tossed the rest. If you can find a minister who's willing to do that I certainly think it's a great way to go.
If you don't want all the pomp and circumstance (and expense) of the ceremony and reception, then simple Justice of the Peace is a cheap, fast, legal way to go.
Try looking for a Humanist Celebrant in your area. There's a search feature by state at the Humanist Society web here.
My wife and I got married in the courthouse officially, but plan to have a ceremony in about a month. Since the ceremony has no legal authority (technically we're already married), we can handle the ceremony however we want!
The downside to this plan is we still don't know exactly what we want. But I'll tell you how it goes in about a month.
It’s easy, get a justice of the peace and a whole group of people together, and get marrieds. Marriage is whatever you want to make of it. Hell, I know people who have thrown themed weddings; I’ve gone to one medieval wedding and 2 Halloween weddings. When i worked for Disney, I even contributed to some Disney weddings.
I got married in the registry office, and had the registrar follow one of the pre-approved scripts without any mention of god :)