Hall Green dogtrack, racing on Tuesday, Friday and Saturdays. Excellent restaurant (for the money) where they have really good service and a man who comes and takes your bets. The restaurant works out at about £15 per head.
This is probably the top football stadium in the area and one of three Premiership ones in the city (at present). I have visited several times with some fond and some not so fond memories of the stadium.
It is possible to have tours of the stadium which are available daily at 10am and 2pm except Saturdays.
The local venue for Test Match Cricket and One Day Internationals. Catch a day/nighter if you can. I sometimes head down here after work... it beats sitting in the pub (if the weather is nice that is!)
Take in a cricket game at Edgbaston or New Road, Worcester.
A great way to relax and see the traditional British summer sport (weather permitting of course!). Edgbaston, in the suburbs of Birmingham, is a modern 20,000+ capacity ground which hosts occasional international games. New Road, Worcester is a much smaller ground but set beside the river Severn and with the backdrop of the famous Worcester Cathedral.
You can watch county games, played over 3 or 4 days, or a one day game played over about 6 hours. If you don't understand the rules, there are always plenty of people to try and explain!
The National Indoor Arena hosts a variety of events including some of the UK's premier athletic competitions.