Guidebooks might be in order to know what to see in Finland. Then, depending on the remaining time and your interests, you a trip to Sweden, or Norway, or Denmark (all part of Scandinavia). I suspect that Stockholm or Copenhagen would be the enough for you remaining time.

My typing is horrible.

Corrections: ... your interests, a trip to Sweden etc.

... enough for your remaining time.

Thanks for the starting points. On the map Narpes look extremely remote so perhaps the car rental sites can help me figure out travel times.

For routes and travel times, try viamichelin.com

Närpes is a small city, you can see it in a day. You have several options to get there: there are few daily bus connections from Helsinki to Närpes taking about 6-7 hours. The nearest Railway Station is in Vaasa and the direct train takes 4h 30minutes. Maybe it would be most convenient to go from Helsinki to Vaasa and rent a car or take local bus to Närpes. There is one hotel in Närpes and several in Vaasa (including Tropiclandia spa hotel). You need to count at least two days for Närpes with the travelling time since it's a bit out of the way.

Helsinki is compact city and you could see the most important sights in two days. I would recommend visiting Suomenlinna (the ferry ride is very nice), Kauppatori and Vanha Kauppahalli. I would advise to get hotel in the very centre of Helsinki so you can walk to almost all the main sights. I can personally recommend Sokos Hotel Helsinki, in Kluuvikatu. Or if you want to watch your budget Omenahotelli (www.omenahotels.com) has two hotels that are in pretty central locations.

There are two company's that operate ferrys from both Turku and Helsinki to Stockholm - Viking Line and Tallink Silja. Both have websites with timetables and online booking. There are sometimes excellent offers, like 10 euros for whole cabin! You can do a 24h cruise where you don't get to go to Stockholm, but will see it from the deck or day-trip where you will about 12 hours in Stockholm. Both also sell packages that include ferry + hotel night(s) in Stockholm if you want a longer visit.

There is also the possibility to take a quick day-trip to Tallinn - there are several different companies that have quick ferries so no pre-booking required.

And if you want to ambitious you could also try to fit in a trip to Oslo as there are now budget airlines offering cheap flights to Oslo - Ryanair flies from Tampere-Pirkkala and Norwegian Air from Helsinki-Vantaa. I have seen both selling round-trip tickets around 20 USD.

There are no budget airlines flying from Finland to Copenhagen, but Blue1 is usually the cheapest - roundtrip would be about 150 eur if you book early enough.