Things to see and do...well this is difficult as I do not know what you like.
Unlike large cities like London, Paris we have few spectacular building and no major river through the city.
There is a web site here with some ideas
http://www.beinbirmingham.com/
and here
http://www.birminghamuk.com/go/attractions.htm l
The following are all in the city centre.
There is a large free museum and art gallery in the city centre
The Sea Life centre
The Birmingham Wheel (like London eye without the views)
Think Tank, a modern science museum
The Cathedral (a rather modest one compared to others)
We have many canals in the centre of the city and many have been "done up" with bars and restaurants.
Near Broad St is Gas St Basin and the canals behind the Convention Centre, they are well worth a visit.
Birmingham has had a lot of work done on it in the last few years and it is now quite a pleasant city to stroll through.