You can go Van Vihar, Manav Sanghrahalay, Kaliyasot dam, VIP road. Around Bhopal you can go Bhimbetka, Delawadi and Bhojpur. Also Sanchi Stupa and Tropic of Cancer.
Bhopal is a nice city. There are plenty of options to visit there in the city. You can find this link helpful. Here you may get all the related details like how, when and where to visit in bhopal with the tickets and taxi details. https://www.youtube.com/playlist?list=PL-7au7SWuGMsDAjPZhFbSXrL7fZlueLaL Apart from that if you have more time, you can visit panchmani as well.