There is a playpark in Breckenridge, but I don't think it had enough water this year to run. It is not a higly regarded playpark by the locals anyway.
Depending on what you consider "close" ... there are still many options.
You have missed the early season Eagle runs and Gore Creek in Vail about 30 to 45 minutes away, but the Arkansas has all kinds of Class 2 thrugh 4 options about 90 minutes away, and of course Shoshone on the Colorado River is the traditional year round run here. It's a Class 3, short run with easy shuttle on Highway 70. Shoshone is also probably no more than 90 minutes from Breckenridge.
Here is a direct link to my first day on Shoshone.
There are also tons of Arkansas River journal entries with photos and videos on the site.
You should really consider Brown's Canyon if you are looking for a fun Class 3 while you are up here.
This is the link to my first day in Brown's Canyon.