In the following directions, North is taken to be the top of the map, irrespective of what the compass says.In Sturmford, it is in the southern half of the town, in the extreme SW. In Drangheim, just inside the walls in the extreme NW. In Guberland, due south from the central square. In Thjorgard, in the north of the main city, just east of the path leading up to the Jarl's palace. In Thronheim, in the east of the main city on a road going north from the road that leads to the Jarl's palace. In Frosgard, in a house just north of the rosd that leads south out of the city. And lastly, in Arslegard, in the east of the city roughly SW of the Tavern.
There is also an "unofficial" trainer up to level 25 (and some "shops") on the upper floor of the Tavern in Thjorgard. The cheapest places to train are here, Sturmford, and Frosgard.
There are no training areas in Yorwick, Lindisfarne, or on the Isle of Ashes.
In every case, you need to talk to one of the people in the training area to initiate the training dialogue. IIRC, official training areas are marked outside by a series of red-on-white roundels.
I know the game, but you need someone else to cope with computer problems.