The whole of Old Rauma is the main attraction — a UNESCO-protected neighbourhood of about 600 wooden houses, mostly 18th and 19th century, still lived in. Walking it slowly is the point. Add the Church of the Holy Cross, the Old Town Hall, and the Rauma Maritime Museum, and you have a solid day.
If you have a second day, head out to the Sammallahdenmäki Bronze Age burial cairns — Rauma's second UNESCO site, half an hour inland by car. Lace fans should time a visit around Lace Week (Pitsiviikko) in late July, when the old town fills with markets, demonstrations, and the famous Night of Black Lace candlelit evening.