explore in there very great Evangelic temples, and even Catholic ones (watch). The oldest are from Medieval period. If you are a fan of exhibitions, you'll find in there many of various galleries about writers, sea, history and so on. Also, you have to go to Malmo, very charming city located at the South part of country - it is next reason to reserve flights to Sweden.
Maybe your relatives came from east of continent, like from former Polish lands, that are now a part of Ukraine? If that's right, you have to reserve flights to Lviv.
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In that city you could find plenty of interesting objects connected to our country, like art exhibitions and another museums. Beside, it has beautiful architecture (explore here). Maybe it isn't so well renovated like buildings in Wroclaw or Krakow, but it's still very pretty.
After you choose flights to Lviv, you could consider to have a trip trough whole Ukraine, this huge country has a lot to offer for tourists.