Go watch a Rugby (http://www.leedsrugby.com) or Cricket (http://www.yorkshireccc.org) match - if there's one on it's a must!Go for a nice meal or go for a few drinks see below in one of Headingley's many pubs and bars.
Take a walk up to the beautiful Victorian Headingley campus of Leeds Metropolitan University or onto Weetwood via the Meanwood Valley Trail into the extensive gardens of the 'Hollies' arboretrum about 15 mins walk from the centre of Headingley.
A short Otley Run or Headingley Mile pub crawl more below is certainly a good way to acquaint yourself with the various watering holes on and around the Otley Road.