We find that Fishing Bridge is the best base camp area for us. As the "Executive" stated, the park is a big figure 8 and you will spend some time going past the same places, but it can't be helped. You will be stuck unless you're towing a car.
On our last trip, we stayed a week and ended up putting 500 miles on our truck. If you stay at Fishing Bridge, take an evening or two and turn right out of Fishing Bridge and drive about 6-7 miles and there is a great turnout that people gather at in the early evening and watch the animals come out of the woods. We took our dinner a couple of times.
We also toured Grand Tetons from Yellowstone. For us, it was no big deal to drive into Jackson Hole and sightsee. When leaving Jackson Hole and heading back to Yellowstone, you'll reach the first left you can take into the Grand Tetons park, take a right instead. This is a great little loop along a river where you'll likely see Moose and more Bison. There is also an old church and a famous barn with the Tetons in the background.
You can pretty much see Teton Park in a day and even do a few hikes. We did 25% of the Yellowstone figure 8 each day and it worked out well.