1. Fly to Prague and then by train. This is my preferred route to get to Ostrava.
o From Prague to Ostrava by train option 1: multiple connections a day via Czech Railways https://www.cd.cz/ Search for Pendolino SuperCity train (the best one with a restaurant), seat reservation obligatory when booking, ca 3h trip, see below the screenshot as an example
Connection Praha hl.n. to Ostrava-Svinov as Praha hl.n. means the main railway station.
You can use Uber or other taxi services in Prague airport to get to the main station down town, it takes ca 40 min. Shuttle bus is also operating, or local transportation to the first underground station and then by U-tube.
If you decide this option, let me know, will give you more hints
o From Prague to Ostrava by train option 2: via Leo Express railways https://www.leoexpress.com/en Multiple connections a day, business is reasonable, premium even better, meals are served from the menu, seat to be selected during booking
o From Prague to Ostrava by train option 3: via RegioJet https://regiojet.com/, not selling tickets yet, take Relax Class there, seat to be selected during booking
o For Option 1 to 3 online cancellations possible until more than 15 min before departure
2. Fly to Katovice (Poland) and then by rental car to Ostrava, 1h15min on highway, easy drive (You can also go to Ostrava by train from the main railway station, by taxi or shuttle bus to get there from the airport. A bit complicated, I would go by car). Besides LH / Polish Airlines / … there are also low cost airlines such as Wizz Air operating from several airports across Europe
3. Fly to Krakow (Poland) and then by rental car to Ostrava, 1h40min on highway
4. Fly directly to Ostrava through Warsaw (limited number of flights, check it out on kiwi.com
5. Fly to Vienna, then by bus/rail (RegioJet as above, 1 or 2 transfers depending on the time and route), ca 5h in good times