In the summer this is a haven in the middle of the city. It is a public garden where I like to go and relax in the grass under a blooming tree. There is also a cafe and a shop here. Before you leave you should buy a bouqee of flowers (you pick yourself in the garden!).
A huge flee market that occures two times a year, once in spring the other in the fall. Take the subway to Solna centrum and take the 3 min walk to the big sports arena where the fleemarket is held. There is lots of retro and vintage and a good potential of finding bargains.
It's been at the same address for the last 80 years apparently and serve some classic swedish food like köttbullar and isterband. Being swedish I guess could I either avoid or cherish this, but I choose the latter.
If you want to try something outside the city center this is a really beautiful small gem. They cook delicious seasonal food and have a nice selection of cheese and charcuterie for your wine. Best to book table beforehand.