any subway routes from Beijing to Terra cotta Museum....?

Hi, actually, the museum is in Xian. From Beijing South Railway Station, you can take a taxi to Beijing West Railway Station, where you can take a train to Xian Railway Station or the Xian North railway station.
If you reach Xian Railway Station, you can catch bus no. 306, 914 or 915 to the museum directly.
If you arrive at the city's North railway station, you can take bus no. 266 to Railway Station first and then transfer to take bus no. 306, 914 or 915 there.

Dagu Fort and Tianjin Cultural Street can not be missed there. You can also go and visit Huangyaguan Great Wall or Haihe River.

Generally, if you just have some regular food, the food in Tianjin is not that expensive. So just go and find one to full up.