In WDW? I think I know where you can tan. If you exit your hotel turn either right or left. Ok, you're there.
Or go straight.
I second the people who have mentioned going tanning BEFORE you go. I'm a tanner, but will go weeks and weeks between a session, and sometimes *I* even will get a slight pinkness on my back, if it's been a long while. It's not a good idea to jump into it, right then and there.
I'd start about a month before, and work your way up from 10 to 15 to 20 minute sessions (Depending on the bed. There are some beds, which the maximum time is 12 minutes, anyways) - probably 2 or so, times a week.
I'd also get a lotion with a bronzer in it. No, no... not a bronzer.... a self tanner. They're about the same level of color as the Jergens one (gradual) but also has properties which will increase your melatonin productions, and vitamins and moisturizers, etc etc. I, personally, really like JWOWW's new line (By Australian Gold), believe it or not.

It's obnoxiously priced in the salon, yet really well priced online:
http://www.amazon.com/Australian-Gold-Bronzer-Tanning-Lotion/dp/B004FEKA3E ~ It's a good indoor lotion, as well as a nice self tanner. I do like it.
There's many places (LA Tan being one of them) that have days which are cheap days. LA Tan has $5 Tuesdays, for instance. Look around for a place which might run deals like this.
I'm not anti-tan. I like having color AND it also helps (for me) with seasonal "I don't feel like getting out of bed" moods.
And as an FYI to the nay-sayers: Everything causes cancer. Everything and anything can and will cause cancer. Responsible tanning, not going crazy and being some kind of lunatic tanner, is not a one way ticket to a headstone.