Been here six years now, married to a Dane, got a kid, work in CPH and live 25k south. I like it and it's a great place to live, but there are some buts... Will you be on local tax or the researcher scheme? Living costs arent that much higher than the UK, apart from cars which are mental. Are you married and do you have kids? If married, will your wife work? How social are you? Once you 'crack' the Danes, they are great. Will the job provide accommodation?
I have seen a lot of expats come and go, having employed many of them. For some it is fantastic, for others it's not great. PM if you want some more info.
As for biking, there is a big scene based mainly around single track. I'm in Spain right now, but otherwise would be getting ready for the annual Merida marathon, a 103 km ride north of CPH with about 3000 entrants. This is the big race but there's other similar rides most weekends. Road biking and running are also massive here.
Let me know if you have more questions...