cheapest and best way from Tianjin to Fairmont hotel in Beijing and cost please.

You can take a high-speed train from Tianjin to BJ South, and the ticket fare is CNY15.5 for a second class seat and CNY19.5 for a second class seat.

When you reach the south railway station, you can take the subway line 4 and get off at Xidan Station, where you can transfer to line 1 to drop at Yong’anli Station. Leave from the Exit C and walk about 450 meters to the hotel. The subway fare is CNY 2.
This is the cheapest way.