Hi Richard
Welcome to Denmark, and welcome to the SVRider forum.
The "bike racing" part of your questions is probably somewhat of a problem. We don't have an awful lot of racing here in DK, unfortunately. However, the MC600 Challenge Cup might be of interest to you. They have a website
http://www.mc600.dk but it's entirely in Danish. You can find the race calendar
here, with dates of the races and which tracks they're racing on. There are still four races left of this season, but they all take place in Jutland, on Padborg Park, Ring Djursland and Jyllandsringen.
We do have track days, but even though they're arranged by Danes, they're still usually held on race courses abroad, very often in Sweden. These are some of the people arranging track days:
Racing4Fun,
Team-Trackday and
Din Ven Bike.
A good place to hang out would be Langelinie. All kinds of people on all kinds of bikes come there, usually in the evenings and weekends. Another place is in Buddinge every Tuesday. Quite a few of us from SVRider.dk usually go there.
There are a lot of good roads when you get away from Copenhagen. The area around Ganløse - Slagslunde - Smørum, just west of Herlev, is among our favourites. Nice winding roads, with fairly good blacktop. I have only lived in the Copenhagen area for a year, so I don't know that much of the countryside yet.
I don't know why so many people here like the V twins so much. The SV is, and has been since it was introduced, a very popular bike. Maybe because it's fairly cheap compared to many of it's competitors. And is also very fun to ride, which you probably know yourself.
I hope some of the above will be helpful. If you have further questions, just ask.