Riga is a great city to visit, there is art in every corner of the Old Town and the other side of the river. It is also a great place to get lost in the handcraft markets where you can find really good handmade souvenirs outside of the commercial one you might foud at the souvenir shops with good prices. The Art Nouvo district is one of the biggest in the world and has a lot of interesting buildings.
Insider Tip:Take your time to visit Jurmala, is only 40min away by train from Riga and the cost is around 1.4 Euros, so is super cheap to go and spend a day at the beach. Go to the island in the middle of the river and visit a neighbourhood of old fishermen wood cabins. Go out at night and enjoy the Latvian night life in different pubs, bars and clubs around old town and city center.