i had 3 years old kid, price range - not so expensive but think of near mrt so that no need to walk further.
if your kid requires a bed, u will need to look for triple sharing rooms. u can indicate 2 adult and 1 children when searching using third-party sites such as agoda or booking.com.
'not so expensive' is rather vague. maybe to give u better idea, business hotels cost around $120 for a double/twin room. there are cheaper options like capsule hotels and hostel that can be less than $50. there are also more expensive hotels that cost a few hundred $.
it will be easier for us to make recommendations if u can provide a more specific price range.