You could take the bike to Ugglevikskällan in Lill-Jansskogen, near Kungliga Tekniska Högskolan. It's originally an old fresh water spring, used in the 18th century as a day trip spa-resort. In the 19th century people from Stockholm gathered there on the first Saturday after Whitsun to drink the healthy water.
The area around Lill-Jansskogen has always been associated with drinking, but perhaps even more so by the notorious pub hosted by the royal huntsman Jan Persson, called Lill-Jans in the 17th century. Nowadays both the pub and the fresh water spring are long gone. But the little pavilion still stands. And it's still a popular place for an outing.
Lill-Jansskogen (map) 26 April 2009