Novy Jicin is a well-preserved historic town less than 1 hour away on one of the frequent direct buses from Olomouc. It is an interesting town in its own right, but the best thing about it is the number of other fantastic things to see and do nearby:
Stramberk is a smallish town with many good examples of the traditional wooden architecture of the region. There’s also quite a pretty square and remains of a hilltop castle, the tower of which can still be climbed for good views over the town and nearby hills. There are many legends surrounding the town, including that of the gnomes that live beneath the hill and the origins of the local pastry known as Stramberské usi, or Stramberk ears (this legend is not for the weak of stomach).
Kopřivnice is the home of the TATRA automotive museum. There are some fairly interesting contraptions, including limousines, across-Africa expedition trucks, all ranges of military and heavy vehicles, racing saloons, and even the odd plane or two suspended from the ceilings. It is recommended even for people without a specific interest in things automotive. There is not much else to do in town, but there is one nice church, and it’s within walking distance to Stramberk.
Příbor is best known as the birthplace of Sigmund Freud, and there’s a small museum concerning the man and his works. The historic centre of the town is also very pleasant, and if you’d like to see a Moravian town that is hardly visited by tourists at all, this may be the place for you. The streets between the square and the tall white tower seem to be the nicest part of town.
Overall, this is a very enjoyable day trip, with something to interest all but the most cynical of travellers.