There are 2 campgrounds on rt 26, just north of the interchange with I-80. One is Fort Bellefonte, the other is a Bellefonte/State College KOA. Those are probably your closest options. Could be at the mouth of Spring in 5 minutes, probably 10-15 minutes for the areas upstream of Bellefonte. I have never stayed at either so I don't have a review. Generally private campgrounds cater more to RV's than tents, though.
Another private campground is 7 mountains, located on 322 on top of the mountain between State College and Lewistown. It's where we hold the jam. They are also a private campground that caters mostly to RV's (and people renting cabins), but they do have tent sites. It's probably a half hour from Spring Creek, but it is a nice central location if you have anything other than Spring Creek in mind. i.e. it puts you in a better location for a trip to Penns or the LJR, or the Kish/Honey/Tea drainages.
Public options:
Bald Eagle State Park has 2 campgrounds. About a half hour to the town of Bellefonte (closer to the mouth, farther to places upstream of Bellefonte)
Black Moshannon State Park has a campground. I've stayed here, and it's decent. Proximity to Spring Creek is nearly identical to Bald Eagle.
Penn Roosevelt State Park - rustic campground. no flush toilets, running water, etc. Tents only. It's a nice place, though, I like this better than having RV's everywhere. It's about 50 minutes to Bellefonte (few minutes closer to areas upstream, farther to areas downstream).
And, umm, that's about it, I think. The nicest campground in the area for tents is Poe Paddy. Remote, just rustic enough, and right on the banks of Penns. But it's a hike over to Spring. Because of the remoteness, you're kind of area committed to Penns Creek and some of it's tribs. Car camping permits can also be obtained for on the state forests. It's not a hard process. But you would be limited to the state forests, none of which are all that close.