I plan to visit Beijing in May for a week, would like what are the neighbouring cities i can consider too

Nearby cities, I think you can choose to go to Tianjin by intercity trains, Qingdao and Jinan. These are all good places to have a look.

For Jinan and Qingdao, the average temperature is around 15 to 22C. Most of the days are cloudy.

For food in BJ, the first you need to have a try is the Peking Roasted Duck. Then you can have a try for local snacks such as the Cream Fried Cake, Glutinous Rice Roll with Sweet Bean Flour, Yellow Pea Cake and so on.