I don't believe either heaven or hell are real places, of course, but if I imagine places (or states of being) worthy of those names, boredom doesn't seem to be a likely problem.
For me, "heaven" is, by definition, a place or state of being which is immensely pleasurable. Since boredom is not pleasurable, boredom simply would not exist in heaven. Even if available activities in heaven were limited and repetitive and monotonous by our pre-death standards, for heaven to truly be heaven, our heavenly selves would have to be immune to, or incapable of, boredom.
Perhaps brief moments of fleeting boredom could occur in a place or condition worthy of the name "heaven", but then they'd only exist to heighten by contrast the pleasure of having that boredom relieved.
As for hell, it is by definition a place of great and unending suffering. While boredom might be one item on a long menu of torments, I can't see it as one of the greater threats when suffering like having all of your fingernails and toenails ripped out while hot irons were stabbed into your eyes and spiders were bursting forth from every pore of your skin would be considered a relief from the more serious torture you'd routinely endure.
Just as with my idea of heaven, where boredom is either very rare or non-existent by definition, in a "true" hell there would be no "getting used to it", no adaptation, no "tuning it out". For hell to be hell, every torment would remain as horribly painful and terrifying the seven quadrillionth time as the first time.
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