The Marriott Courtyard in Sai Ying Pun on Connaught Road offers harbour views on booking.com at HK$1500 plus 10 percent, which comes to around US$200. It's about a ten-minute walk to the MTR, and it's not a touristy neighbourhood. Those are drawbacks, but finding a harbour-view room for US$200 which doesn't have a drawback or two is pretty difficult. (Search around and you may be able to beat the booking.com price.)

Myself, I wouldn't downplay the attraction of a harbour-view room; it can be mesmerising.

(Also, just scrolling through booking.com, I see there's also the Butterfly Boutique in the same area, which has harbour-view rooms for quite a bit less than the Marriott, though I don't know anything about that hotel.)