About a month ago, we stayed at Ancient Cedars, just across from the park entrance. It was satisfactory. I don't recall about cell service and Wi-Fi. And we don't do TV. The female half of the park ownership is a fountain of knowledge about the area. You might call and ask your questions. Some of the other contributors to this thread have a link to Ancient Cedars with a phone number.
There is camping in the park but only 15 sites with full hookups that are reserved months in advance. Another place to see nearby is the town of Aztec, which is similar to Mesa Verde but on a much smaller scale. However, you can walk through all the structures, a big plus. We thought it worth the visit. It's maybe an hour from Mesa Verde