Sang Nila Utama Museum is the best place in Pekanbaru to get a quick grounding in Riau-Malay culture. The collection includes traditional dress, wedding objects, toys, musical instruments, and everyday artifacts that explain the province better than another mall ever could.
It is a provincial museum, so come with realistic expectations: useful, sometimes old-fashioned, and more interesting if you already care about Malay culture. Pair it with An-Nur Great Mosque or Soeman Hs Library.