Just seen this, I'll try and offer some suggestions. Stockholm is my speciality though.
Cheap airlines, well Ryanair fly into Skavsta airport (about 75 kms south of Stockholm), and there is a great bus serive which gets you into the city centre. From Stockholm, you have access to the archipelago, which is just beautiful. There are daily boat services which take you out there, so you can pick your islands depending on what you want. Many of them offer camping or cottages (stuga), even the od hotel. more information on island hopping.
There isn't a great deal to do on these islands, but if peace quiet and relaxation are what you're after, then you have it in abundance. And it is beautiful, of course.
This is a good link for info on Stockholm.
BigumyandThob is quite right about the school holidays. July is the big holiday month here, lots of things are closed, and the city is tourist central, so August is a much better time to come.
Let me know if you want anything specific answered.
Vintage- CAT me