The Little Miami doesn't have as many big waves and play features as it's bigger brother, the Great Miami. Most playboaters will hang out around Boathouse Rapid and paddle back up to the put-in for a quick park and play session. However, there's still decent play to be had depending on the river levels.
The other major difference between the Great and Little Miami is the scenery. From a river health perspective the Great Miami is no worse than the Little Miami (the Great Miami may be better...), but the scenery is less than to be desired. The Little Miami river is a National Wild and Scenic River with limited views of developed areas, abundant wildlife, and good fishing.
The put-in is at Kelley Nature Preserve (the same as for the PnP at Boathouse) and the take out is at Jim Tarrell Park in Milford. The rapids don't really have 'official' names (with the exception of Boathouse), so they are named based on how I identify them on the river.
If you don't feel like driving to the Great Miami and the Little Miami is around 6 feet, this is an easy and fun alternative for the east-side boater (provided nothing else is running). At 5.2ft and below (Milford Guage) you will find that nearly none of the rapids are running, with little to no flow in large portions of this section. The only rapids you can expect to be running are the two close to Milford.
The entire Little Miami River below Clifton Gorge is legally runnable. Below the listed take out you can continue to paddle all the way down to the Ohio River. It just tends to have even less whitewater and involves lots of flatwater paddling. (I wouldn't recommend a playboat if you choose to extend your trip thusly.)