You need a minimum 3 days to visit Hyderabad but I'll say you should have 4 days. Out of these, reserve 1 full day for Ramoji Film City and one evening for Golconda Fort (Light and sound show is a must watch). Other than these, you should not miss Charminar, Salarjung Museum, Buddha Statue inside Lumbini Garden and build in the Hussain Sagar lake. If you have some more time go for Birla Planetarium (it has a huge dinosaur skeleton), Qutubshahi Tombs, Snow World, Chowmahalla Palace.
Places famous for food - Paradise biryani, Bawarchi biryani (if you are a non vegetarian), Pista House, Nimrah Cafe for Irani tea and Osmani biscuits. In the end, visit the Karachi bakery and shop for your favorite biscuits.
Shopping - The Laad Bazaar around Charminar is the best place to shop. Use your bargaining skills to get the best prices.