This is a great city. Like Beijing a national city with a long history, boasting of the oldest university in China and a significant imperial past. The bridges and rivers are beautiful. It's cheaper than Beijing but less accessible by public transport despite a high speed rail link between the two.
I was told that Tianjin wasn't worth a more than a day trip from Beijing. I disagree! I really liked this small city. This place has breweries, bars, cafe's, and culture. I enjoyed my three days there, and there is also a way to access the great wall ! I wouldn't cross it off your list, just add it on to the end of your Beijing trip.
I love Tianjin but I've lived here for six months now. It's a great place to live but there isn't a lot going on if you want to make a week trip of it. You are better off going to Beijing.
Tianjin people is more friendly and simple. 10 years ago most of them are cycling to work, but now many have their own car. They do have famous food like 'Gou Bu-li Bao-zi' and 'HuaJuan' biscuits. Never and less pay a visit to food Street, Fashion Street and Ancient cultural Street.