Where can we show off our new Swing and Ballroom dancing skills?

Great idea. I can't wait to go and see this!!! Thanks.

How about an afternoon tea dance at the Royal Opera House in Covent Garden? One or two of the more upmarket hotels eg the Waldorf do similar.

http://www.timeout.com/london/dance/event/39564/tea-dance#details

Don't forget Vienna Balls!
It would be a mistake to only think "waltz" when you think of a Viennese Ball. Most of the larger balls have rooms with different types of music: rock, Latin, etc. Although, yes, there is plenty of waltzing too. The ball season used to traditionally run from November til about Easter (with the real high point being January and February --relief from the long dark, cold winter.) But, practically speaking, it has now expanded and stretches into the summer. During the ball season there are literally hundreds of balls, ranging from big and glorious in the royal palace and the city hall, to small balls in hotel ballrooms. Balls are often hosted by specific professions, i.e., the Coffee-makers ball, the Lawyers Ball, the Florists Ball, etc. Some are broader in concept: the "Trachten" (traditional dress) ball, The Rainbow Ball (Gay ball), etc. Regardless, tickets are generally available to the public. Most years, my wife and I will go to at least one ball. We'll meet a group of friends for dinner and then we all go to the ball and dance til 5am. With everyone wearing tuxes and ball gowns, it is very fun and special. Balls are such an integral part of Viennese life. Be sure to order your tickets well in advance. Generally speaking, in Vienna the language barrier is quite low. Many (or even most) speak English pretty well. Have fun!

In one of Rick's videos of Paris he visits a jazz club where there was swing dancing.
I met a French girl here who told me there were salsa cruises on the Seine.
Believe there are over 40 Salsa clubs in London alone. I went to a Salsa club in Brighton.
Ron in Rome posted that the barge Tiber where Audrey and Greg danced in "Roman Holiday" is still going during the summer months.However I don't believe you will find them dancing Line of Dance though.
What really surprised me was the fantastic dance floor and dance music(they played everything from Sambas to Waltz) on Silja cruises between Stockholm and Helsinki.

Caveau de la Huchette (sp?) is a jazz club near St Michel metro in the 6th. It has swing dancing and is a really fun place (very inexpensive). I believe that it may be the club in Rick's video (the club to which the previous poster refers).

Best to google the type of dance and city and you will see lots of options depending on what night of the week you will be there.

London has so many venues in all categories.

My dance partner and I spontaneously dance in front of famous sights all the time. Last night was waltzing to a busker playing Tennessee Waltz on the sax in front of Charing Cross Station. My birthday was tangoing near a waterfall in Iceland.