The Blue River has several sections that can be accessed, they are all mostly class I runs, but the area below Rothrock Mill has a few class II rapids. The river is wide enough that downed trees are not usually an issue. The Indiana River Trails site has an overview of the different sections. But note that the Stagestop campground mentioned on their site is no longer open, and you should plan to take out at the Blue Chapel takeout instead. Also note there is an access point not noted on their website called White Cloud, which is at the very end of Harrison Spring Rd, but limited parking makes it fairly useless for group paddles.
The most common section to run is Rothrock Mill to Blue Chapel. This section has about 3 class II rapids and several class I rapids. It's about 10 miles long and takes 3-4 hours. Below Blue Chapel are a couple of more class II rapids, followed by a several mile long pool created by the Ohio River.
From Milltown to Blue Chapel there are many gravel riverbanks that would be suitable for camping, though they are rarely actually used for that purpose. Most of the area along the river is private property which makes the banks fairly undesirable for overnight trips.
Rothrock Mill Rd NW, Depauw, IN 47115
Put In https://www.google.com/maps/dir/Louisville,+KY/38.2728921,-email@example.com,-86.2910272,107896m/data=!3m2!1e3!4b1!4m8!4m7!1m5!1m1!1s0x88690b1ab35bd511:0xd4d3b4282071fd32!2m2!1d-85.7584557!2d38.2526647!1m0