Once you start bunny proofing, it won’t be all that hard to hide the cords (you can use NIC grids to block off areas, or just put the cords in cord protecting tubes). Still, I personally wouldn’t have a bunny in my room. First, lots of people are allergic to the hay (much more than the bunny itself) so if you’re sleeping around hay 8 hours a day a minor allergy could become much worse. I have minor allergies to the hay which don’t bother me at all since I’m not around it for so many hours.
Second, bunnies are really loud at night. They tend to be up and moving until well after midnight, then they’re up again and playing at 5am. The few times the buns have slept in my room I didn’t get much sleep. A super sound sleeper might be fine with it though.
I think either place would be good if the dog really wouldn’t be able to get in with the bunny. Even if your plan is for the dog to never see the bunny, I would do some training with him just in case. You can work on teaching “leave it” and getting him calm when he sees the bunny (keep the dog on leash and bunny in a cage). The dog doesn’t need to be friends with the bun, but a basic understanding of “There’s the bunny, I need to be calm now” would be a huge help if they accidentally got together.
Do you spend time in the basement? If it’s a common family hangout area, it sounds like a good fit. If nobody ever goes down there, then the bedroom would probably be better. Like the others said, a huge cage is absolutely necessary (the pet store ones aren’t worth it unless you’re going to attach an exercise pen to the outside).