Whenever I know I am travelling to a new city, I create a list of potential things to do.
Here’s the list of online searches I do to discover some off the beaten path or must do tourist activities. I put in the city’s name and then:
Time Out - Time Out is a great resource used by locals to find out what is happening in their city. Not all cities have a Time Out magazine, but it’s always worth a check.
Festivals and the month you are going –  This will should provide you a list of upcoming festivals that month.  
Your specific interest– I always search for cooking classes, breweries, best restaurants. You may want to enjoy hiking, biking, kayaking, wine tasting, concerts, breweries, etc.
Must do - I have found some great top ten things to do lists this way. I like to mix tourist must do activities with things locals enjoy.  
Tours – Searching for tours in the city can bring up some fun options like food tours or ghost tours.
Sporting events / Concerts/ Plays – Ticketmaster or Stubhub is a great resource. You can look at the dates you will in town and see if your favorite band happens to be in town.
I also check out travel guides from the library to see if I like the format and the information and then order the most current edition. If a guidebook is more than 2 years old, I will rely almost entirely on online information – especially for Maps.
How do you research fun things to do when you travel?