Ivan, Hyderabad is perhaps the first place where the opening of the new international airport led to the coming of numerous radio taxi services of varying choice of prices and vehicles. You dont have to worry about the availability of radio taxis from HIAL. Check the following:
Call Taxi, +91-40-2790-1111/1122
Cel Cabs, +91-40-2324-2526
City Cab, +91-40-2776-0000/6631-6000/6631-6001
Euro Cabs, +91-40-2351-1888/6673-8882
Fast Track, +91-40-2888-9999/2760-2760
Green Cab, +91-40-6664-4444
Hyderabad Cabs, +91-40-2330-3324/3245-5055
Metro Cab, +91-40-6610-0676/0677
Orange Cab, +91-40-6631-5555
Dot Cabs, +91-40-2424-2424/+91-98-481-42424
Easy Cabs, +91-40-4343-4343
Meru Cabs, +91-40-4422-4422
The rates could vary between Rs. 10 and Rs. 18 per km depending on the type of vehicle. HIAL to Nampally would be between 22-32km depending on the route you choose. I suggest you take the route via Srisailam Road (not sure if there is a link up yet). This will be shortest via Chandrayanagutta etc. Else via Mehdipatnam would be around 35km. So, your expenditure will be around Rs. 550 which will be lesser than Aero Express and obviously more convenient as you can reach your door step!!!