There are a few classics, and of course, if you are a music fan, that means you won;t be having Whitney / Westlife / Celine, or any other over-egged warble-stranglers!
I love 'I Hope You Dance' - the Lee-Ann Rhymes version of course, not that Keeting garbage!
You could go for some classic doo-wop - 'Blue Moon' by the Marcels fits.
'Dancing In The Dark' by Big Daddy is a doo-wop version of the Springsteen classic - nicely off-beat, let me know if you want it, I'll copy it for you.
If you don;t want the traditional 'slowy' - which are usually sad - then you could go to the other end of the scale -
'Don't You Just Know It' - Huey' Piano' Smith And Ther Clowns will have everyone smiling.
'Words Of Love' by The Beatles is an unusual choice, but it does work - seen it as a first dance, went down a storm.
There's a few - plenty more if you are still stick!