We've been to the Black Hills twice and stayed in Custer both times. It was not as touristy as Keystone, which I think is the nearest town to Mt. Rushmore. It's about 30-40 minutes away, but it's just down the road from Custer State Park, which is an amazing place to see wildlife (bison, pronghorn antelope, etc). It's also handy for the Needles Highway and Iron Mountain Road - both very scenic drives. Wind Cave National Park is not far south of Custer and is another good place to see wildlife. You can also take a guided tour of Wind Cave, which we really enjoyed.

Hey- SD means San Diego.

Keystone is rather "touristy" - I would suggest Custer or Hill City for your interests. May & June are good, although there's a greater chance of rainy days. July & August days are usually clear & beautiful, but can be hot. Things to see: If you're interested in wildlife/scenery, don't miss Custer State Park, Iron Mountain Road & the Needles Hwy. You can take jeep tours there if you'd like to go off-road, too.
East of Rapid City 1-2 hr drive are the SD Badlands (different scenery) - go West approx. same distance, is Devil's Tower. Don't miss Jewel or Wind Cave for different "scenery", but be sure to reserve your tour times, as they get busy. (Great if you have a rainy day). Mammoth Dig Site is also good for a different viewing of ancient "wildlife", as well as a rainy day or hot day break. You'll have lots to do & see - have fun!

I would split up your trip and stay in 2 or 3 different locations, rather than pick one place and stay there the whole week. Driving an hour or two or more every day to get somewhere is not worth the hassle, especially with summer tourist traffic on those roads.

Personally I would vote for staying a couple nights in Badlands NP, another couple nights in Custer State Park and then the rest of your time somewhere central to everything else that you're interested in.

There is in park lodging for both Badlands and Custer. Nothing beats being right there in early morning/late evening for wildlife viewing and great sunrise/sunsets.

For birding/waterfowl, seems like national wildlife refuges are your best bet. The only one in the area is Bear Butte - the National Wildlife Refuge website doesn't have any info on it, just a dot on the map. You would have to do some digging to find out more - it's located near Sturgis and looks like it's adjacent to Bear Butte State Park?

Also, since I mentioned Sturgis you need to avoid planning your trip for the same time period as the Sturgis Motorcycle Rally (August 6-12 in 2012).