Yes, TST is the shopping area but with the budget of HK$600-HK$900 per room (for 2) per night, the choice would be a little bit limited in TST.
Also, the chance would be better if you choose to travel during Mid-May until end-June and you could probably forget about April till early May, October till Mid November and probably End-December
If you do choose to travel during mid-May to end-June, you could have a look at the following...
Butterfly on Prat - 3 stars in TST. the hotel is somewhat new (a couple of years I think). The price might be a bit max to your budget
Chelsea - 3 stars in TST. newly renovated / revived hotel after empty for over 10 years. not much information i could gather. still a mystery to me but i think the price might fit to your budget. right next to MTR
Metropark Kowloon - 3 stars in a residential area in Mongkok. rooms are a bit worn, not very close to the MTR (about 15-20 minutes walk)
Metropark Mongkok - 3 stars in Prince Edward. rooms are considered larger in this catagory. across the road from Prince Edward
Standford - 3 stars in Mongkok. old rooms. next to the Ladies Market and MTR (about 5-10 minutes walk)
Dorsett Seaview - 2-3 stars in Yau Ma Tei. in the middle of temple street market. 5-10 minutes on foot to MTR. small rooms with very low ceiling. rooms are old as well
M Hotel - 2-3 stars in Yau Ma Tei. next to the temple street market. half a block away from MTR. New hotel
YWCA Anne Black - 2-3 stars in the residental area in Mongkok. very basic hotel. a bit of a distant to MTR (about 15-20 minutes walk). Cheaper for rooms without bathroom (share bathroom)
Ibis - 3 stars in North Point, a residential district on Hong Kong Island. a couple of blocks away from MTR. very small rooms but full harbour view rooms available which is rare in this category of hotels