I remember once coming across, while browsing some bilingual dictionary, the noun "swing" pointed up as an AmE equivalent for "circuit".
But, sadly enough, what the bilingual dictionary didn't say was if this usage had any currency at all in modern day AE -- and if it was to some extent more common than the term "circuit", as well as appropriate to use for both a short round trip and an extensive circular tour.
In addition, how does a swing differ from a circuit and from a round trip?
You might want to consider the following sources for this.
http://www.merriam-webster.com/dictionary/swing (head to Definition 6b by the bottom of the page)
http://dictionary.reference.com/browse/Swing?s=t (head to BOP also)
The prince and princess, winding up a seven-day swing throughout the US... source