If you can get your son interested in reading and books, that will eventually be a great occupier of his time. 7 is a little young for chapter books, but once they start reading those, it's a great, wholesome way to entertain themselves. All my 6 kids loved to read! I still have two girls at home who are 9 and 11. We have no TV at all, but they love to read!
Regarding the "I'm bored" statement by youngsters: I think it's a perfect time for some 'occupational therapy', which in old fashioned lingo is called 'chores'. 7 years old is a good time to start teaching a few useful tasks around the house, don't you think?
It will be a help if you do provide some structure for him, such as by enrolling him in some type of recreational program. It will be important for him to learn, over time, how to plan his own time and how to interact with his peers. But this is not going to happen overnight, and the situation will only continue to frustrate you if you let the status quo prevail.