I was just doing exactly this for the past three days. It was hot (90-100) on the valley floor, but totally doable if you stay hydrated.
Hiking: I found modern hiker helpful. http://www.modernhiker.com/area-maps/death-valley-national-park/ We did golden canyon to Zabriskie point. Lots of badlands fun – it was hot, but the scenery make it worth the sweat. There were signs to follow the whole way. Our second official hike, not on this list is perfect for the time of year: Wildrose peak. Goes up to 9,000 feet so you are above the heat. Amazing views of badwater AND Whitney from the top – lowest and highest. Easy to follow trail, 4.2 miles each way; 2,300 feet up.
You could try for Telescope peak if you are feeling more ambitious, but there was still some snow up there and you need 4WD to get to the trailhead. Also, I did not do, but have heard there are really cool upper falls if you scramble/climb up past Darwin falls.
Camping: Texas Springs – slightly removed from the bustle on furnace creek, but still pretty packed in and busy. Very convenient to badwater/Zabriskie, Dante's view etc. Mesquite – much quieter and a bit cooler because of elevation. Amazing view of the night sky. Very peaceful. Close to the crater (1.5 mile hike around, worth at least taking a look). Wildrose – we didn't stay, though I wish we had it's tucked in a valley up in the hills. Also, the last of the flowers appear to be up in this direction. Avoid Panamint unless you are into cramped campsites beside the highway with the biker/jeep rental crowd.