Hurray! I have an apartment now.
It is located in Solna, which is not far from Stockholm center which is considered "Stockholm Stad", so Solna is just a suburb or separate Kommun. It is like small city with own Mayor, Budget, Taxation (Solna has minimal taxation level among all Stockholm related kommuns) etc.
Apartment is not new and requires our attention to be cleaned and refurbished after its owner has spent over 15 years there. I even received a discount from him from first month payment due to that ;) It is located on the last 6th floor (that was always in my dreams to live on the last floor) of pretty old building in a very green and quiet (thanks to the windows which lead to the yard) area. Apartment has 2 rooms with area about 65 sq.m.
Owner is an aged Turkish guy who is married second time and is moving to Turkey for a while. So he agreed all details with Land Lord and is allowed to sub-rent it to me for 1 year with a price of SEK 7,000 plus electricity. The price is adequate.
So, I'm returning to Copenhagen and planing to get the family to Sweden on June 7th. Very excited about that!
Literally translated from Swedish it means "day rain" which obviously means what it says - it is so common in Sweden to have rain pouring for a day or so. 
If you are visiting Stockholm and staying in Clarion Hotel at Slussen (Södermalm area) you should not miss fabulous swimming pools complex Eriksdalbadet placed just behind it. All you need is a good will, 90SEK for one time visiting fee, swimming shorts and towel (which you can take from hotel;) You will get 3 hours for swimming in 25 or 50m pools, taking bubble-bath or sauna.
It is very useful to have at least one 5 krona coin in you pocket when you are in Stockholm. This is universal key which will open many doors for you, mostly in toilets over the city. Like in malls - Gallerian or NK, McDonalds (you have to pay for toilets here and 5x1 krona is not always working) and so on. Also it will give you possibility to take a trolley in a ICA and other supermarkets.
