Beijing - Datong-Tianjin

I need some help on planning my November visit to china:-
My plane will touch down PEK either morning or afternoon. But I am not able to catch the morning flight
from PEK to datong and have 2 option, either to stay a night in the hotel near the airport and catch the next
morning flight or take a train about 6-7 hours to datong.
1)which is better ? If to fly from PEK, which terminal should I go? If to catch a train to datong, which
train station?
2)I might stay at BJ for 2 days after my trip in datong , any recommendation of average hotel ?
3)I have been BJ in 2 years back and I am interested to visit Tianjin. Is Tianjin interesting? Should I stay in Tianjin
for a day or 2? before I depart in PEK?
4)How is the weather in BJ and Tianjin?
5)Any vegetarian restaurant in BJ and Tianjin?
Thanks.