We stayed at a hotel south of the park with Internet access, but it was crazy expensive. They have Internet access (for pay) in some of the lodges in the park. Plus there's a library with networked computers, but they limit the amount of time you can spend on those.

It would be wonderful to spend a week or more at the park, because it's so relaxing. But the best bet is probably just to spend a few days there without the computer.