For one, you can head to the 2012 Summer Olympics' white-water rafting track just outside of London, and suit up to join a raft on the rapids. We've done it and survived, and first-timers are absolutely welcomed.
Another option is to make plans to visit some of the older Olympic parks, which most host cities maintain as sports and public event venues for decades upon decades. Cities like Sydney, Athens, and Beijing will be more than happy to let you into their Olympic parks, but our personal favorite is found in Munich, Germany, since you can pair a stroll there with a visit to the neighboring BMW Museum.
However strong or weak your Olympic fever, just reminder to mark August 5 - 21, 2016 on you iCal as the dates for the Rio games, and for what will likely be some of the best Olympic background scenery yet. Armchair travel much?