A few years ago I held an Olympic-themed birthday party for my daughter who was turning four. Her name is Taylor, so we called it the 2005 Taylorlympics.
You can easily substitude any kid's name -- i.e., Carterlympics, Ashleylympics, Tessalympics, Johnnylympics, etc. The kids went from one athletic" station to the next including a (very) short foot race bowling (kids bowling set that she'd rec'd for her 3rd b-day) gymnastics (think somersaults on an exercise mat etc.) basketball (kid-sized hoop) long jump (using a tape measure on the floor) and musical chairs. I made inexpensive T-shirts with easy iron-on transfers from Wal-Mart which was also the "give away". And at the end all of the athletes got a gold medal (picked up a bag of 20-ish for a couple of dollars at Wal-Mart) and sport-themed balloons that cost 50 cents from the dollar store. It was a huge success the kids had lots of fun and it was relatively inexpensive."