Lysa Hora, the highest ,mountain in this area, is high and in winter many people climb up it to ski down it after a bowl of soup and a beer or a hot wine. Stunning views and it's pretty to look at from afar.
The single trails park also provides plenty of scope for walking and exploring the Bila mountain. The website is in English and the area is easy to access by car and there are regular busses up there too.
This link will take you to a top ten highlights of Ostrava in German. A blog made by fellow world traveller. Quite honestly I think their top ten is very well put together. The Svet Techniky comes highly recommended though their website certainly doesn't portray just how interesting and fun this place is for adults and children alike. This is the website link: http://www.stcostrava.cz/web/guest/hlavni-stranka