We believe we Christians will spend eternity with God. No disrespect meant, but sooner or later, wouldn't that grow old? Maybe the first few years or centuries would be great, but with infinite time, wouldn't we grow weary even of Him?

If you're on the right track, of course, then no matter how interesting or stimulating it might be to bask in his presence, heaven would eventually be more of a punishment than a reward. So I want to take the question seriously.

I believe you may be confusing God with us humans. If we conceive of him as a souped-up human being—extraordinarily interesting, highly knowledgable, entertaining, engaging—then we aren't grasping the biblical picture of the Deity. "He is not a man" (Num 23:19). “For my thoughts are not your thoughts, neither are your ways my ways,” declares the Lord. As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts" (Isa 55:8-9).

Let me offer an earthly illustration. Pondering your question, I thought of Darcy, our Bernese Mountain Dog. (Of all our pets, this has been our favorite.) Darcy loves human companionship—and thrives on it. True, as much as she loves to play, she does grow tired, but even then her preference is always to be with us.

Does Darcy ever grow weary of us? It hasn't happened yet. Would she ever grow bored of being with her human family? I doubt it. I believe this is true, in part, because we are not fellow canines. There's a huge gap—emotionally, intellectually, spiritually—between her and us. Even with infinite time, presumably she would always remain a dog. And if we could explain the prospect to her—that she could dwell in the house of her masters forever—I am sure she would offer unending affection and thanks.

In this analogy, you and I are the dog. Not God.
And Amen.