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Golkonda Fort
If you're interested in looking at a fort, then I can suggest you Golkonda Fort. It is almost 11 Km from city center, but the distance will of course depend on the area, you're staying in. The fort had a vault which stored world famous Kohinoor and Hope diamonds once.
The fort itself is an impressive structure and quite huge, giving you a lot of opportunities to explore around, photograph the place and around. The fort overlooks the city, so you will get vantage poitns for having a look at the city.
Hussain Sagar Lake
The man made lake has a lot of structures and attractions around it. Most notably being the Buddha statue in the middle of the lake. You can enjoy a clear evening around the lake, with sunset presenting beautiful scene.
Apart from these, you can check the route and attractions for some heritage walks inside the city, which cover monuments inside the city. The official state tourism department website lists 4 routes. You can check this site, to explore more about the route and attractions.