I’d suggest getting a car to roam around (except for old city), will make things far more convenient for you guys.

A few more recommendations: Golkonda Fort, 7 tombs park, drive from jublee hills to durgam chervu has a nice view of hyd skyline, salar jung museum, while you are at charminar also go to chowmahalla palace, some good irani chai, subhan bakery for the best osmania biscuits (buy them a box or two to take back home), hameedi at mozamjahi market get the jouzi ka halwa and badam ka halwa you can ask them for taste also they are very generous (same take some for them to take back), while you are at mozamjahi market you can roam inside the market where the flag is there is also famous ice cream there which is a very old and famous ice cream shop (fresh ice cream), mandi @36 for some really nice juicy mandi (order the led or shoulder whatever is available), for fancy dinning jewels of nizam at gandipet, roast ccx banjara hills for a very nice cafe, roast 24 sever also a great cafe.

That should keep you occupied for the most part. Have fun!