Denise,
We loved going for lunch( not open for dinner) to one of the covered produce markets Ostermalms Saluhall. I remember there were more than one cafes/ restaurants within the market. I think we had lunch at Lisa Elmquist. Delicious salmon. The market was beautiful, all that fish and fresh produce.
For dinner we went to a great restaurant( a bit pricey ) in Gamla Stan. I remember we went down into a cellar like restaurant, very cozy. I can't remember the name. I'll try to find my credit card records.
Another more casual place we went for dinner was Bakfickan, behind the ultra expensive Operakallaren with which it supposedly shares the kitchen. We liked it a lot.