Olympia is a fun city, and the best resource for fun is Experience Olympia.
You will not want to miss these yearly events:
...and parks...
Some favorite Olympia parks:
Tolmie Park 7730 61 st Avenue NE Olympia
Burfoot Park 6927 Boston Harbor Road NE Olympia
Squaxin Park (formerly Priest Point Park) 2600 East Bay Drive NE Olympia
Brewery Park at Tumwater Falls (with Fish Hatchery)
Washington State Capitol Campus
National & State Parks Near Olympia
Mt Rainer National Park (1.5 hours from Olympia)
Mount St Helens National Volcanic Monument/Washington State Park (2.2 hours from Olympia)
BEER!
Olympia Beer Commercial 1966 (sorry about the YouTube ads)