Though the current basilica and other buildings are fairly new (by European architectural standards), this location has been a holy place for more than 800 years. It was more impressive than I expected.
If you go...
Velehrad has good connections by bus from Uherské Hradiště or Staré Město. Also consider combining the trip with a visit to Modrá, right next to Velehrad, with its folk skansen and the Živá Voda ecology center and aquarium.
And if you go in spring, you might see this in the pretty little lakes there: