If you have a car you should definitely visit Olhava http://27crags.com/crags/olhava
as its the best place in Finland - about 3 hrs from Helsinki. Quite near (closer to Helsinki) is http://27crags.com/crags/reventeenvuori
which may be the second best place (I really don't understand how we got to the bizarre situation of the crag being listed on 27crags but no info being there - you can probably find a copy of the topo guide book, but that is now hugely out of date for Reve. Probably best to go and just ask other climbers what is what!).
Basically you can camp anywhere that isn't a farmer's field or someone's garden: http://www.ymparisto.fi/default.asp?con ... 532&lan=EN
But you can't light fires and of course you must NOT leave any litter or mess. Some crags say "no camping" at the crags, although I'm not sure how that balances against the 'everyman's right'.
The other very nice area is Kustavi, NW of Turku - the cliffs are smaller there, but there are many many cliffs and hundreds of great routes. There are very few sports climbs though, most are trad cracks. All the topos and maps for the Kustavi area: http://www.jammi.net/kalliot/index.html