You can visit the biggest islands around Rauma by a water bus and also smaller islands by private boats. Most small islands are owned by private people so you shouldn't go there without their permission. If you're used to the Greek islands or some others that have a lot of hotels & shops, islands in Rauma aren't the same. There usually is one small café and otherwise it's just the nature. Very relaxing.
When you get to know Old Rauma, it's easiest to walk. That way you can explore all the streets where you perhaps can't drive a car. A bicycle is also quite a good idea if you want to see a bigger part of Rauma; and car in the areas out of the center. Also the public bus service is very good but one trip in the town costs 2 - 2,20 €.
The only way to come to Rauma - or to get out of here - is by bus if you don't have a car. There is no passenger trains to / from Rauma. Well, there is a train but you'll have to travel by bus the rest of the trip to Rauma. You can get from Helsinki to Rauma in about 3,5 hours by bus and by car it takes about 2,5-3 hours. If you arrive to Finland via the Helsinki-Vantaa airport, there are some daily buses to Rauma direct from the airport and some to Pori in which case you have to exchange in Huittinen into the bus to Rauma.
The best way to get to Rauma, if you don't have a car, is by bus! I don't know how efficient and/or nice the trains are in Finland (I suppose they must be great) but the buses are really punctual, fast and comfortable, and I think the price of the ticket is lower than what you'd pay for a train ticket. Anyway, while on the road, you'll see several of these signs along the way! I love them!! :)
Rauma is really only connected by road. There's a marina if you're the sailing type, and adventurous spirits might be able to hitch a ride on cargo ships bound for Rauma, but by and large, Rauma can only be reached on wheels. The lack of a passenger train connection is a big drawback to Rauma's connectivity with the rest of Finland. The bus connections, at least, are frequent and if you're driving on your own, the city's not hard to find. :)
Rauma's public transport system is not excellent. Its operating hours are on the short side (especially in the evening, I think the service ends around 6-8pm or so) and it doesn't go to very many places in the city. If you're staying in the city center, most of what you'll need are within walking distance, but I would really recommend renting a car, or having acquaintances who'll show you around in one. Especially the nature around Rauma is in my opinion a nice thing to see with a car, but don't forget that the best way to experience the city center really is by walking!