Personally I like hunting out shows, exhibitions, tech conference, etc.. that happen to match up with my work trips. Coming from Perth we missed out on a lot that even the rest of Australia gets.
Had a few successes.. you may guess I am a techy and a star trek fan...
Big Bang Theory: Live audience during the taping of season 2 (~2007), back before the insane popularity of this show. Got signatures from several cast, saw a shirt-less Penny and literally walked through the door as it was sealed after struggling get a Taxi from LAX to Hollywood in peak hour without a working phone service. Was my first ever international trip for work.
BarCamp 2.0 in Los Angeles (2007).. was the second event that started off the trend of "unconference" events where a bunch of tech people rock up and do impromtu unplanned presentations planned with sticky notes on a wall.. received an awesome "H2Go" drink bottle that is the best drink bottle I own or have ever seen to date.
Star Trek: The Exhibition - Phoenix, Arizona (2009) - Had just opened on it's second stop in over 10 years while I was in Vegas.. flew in the morning, out in the evening on the way back

Museum kindly stored my luggage lol! Very sadly I missed Star Trek: The Experience in Vegas by less than 2 years. Still sad about that to this day. At least I still got my shot on the Enterprise bridge, as they had the 2nd set here.
RubyConf - Manila, Phillipines (2016) - Happened to start the last day I was in Manila just a few months ago, didn't realise until the morning of when I saw someone post about it on Twitter.. it was only 15 minutes away! Got to meet one of my favourite speakers, and the organiser kindly let me in without a ticket for a few hours. Had to leave at 4:30PM to make my 8PM flight, oh Manila traffic..