As a Christian, i guess, for me, as the Bible states for us, Heaven will just be like Earth except prettier. Without sins, sickness and worries. In a nutshell, as C.S.Lewis aptly put, "as if every blade of grass meant more" (i might have paraphrased this line since i dont have my source with me)
Ps. I dont think there's other dimensions. Though i used to be uber fascinated with the mere thought of it when i was younger.