Finding an accommodation in Stockholm, especially inside the city is a nightmare due to its lack of availability and the price (especially for academics). I had to move four times at the first month in Stockholm. So moving several times is common here.
Below I listed several options based on my preferences (as a postdoc here) for accommodations especially for visiting researchers in Stockholm:
To my experience, Wenner gren apartment is the best apartment but it has really long queue, so you need to apply immediately. Please check the requirements for WGC before you apply!
For Stockholm Bostad you need to pay a registration fee, but for Botkyrkabyggen is free. For the blocket website, please be careful for scams. Always meet the landlord and see first the apartment, and discuss with the locals. Don’t send money before you see the apartment, don’t trust photos etc. If it’s too good to be true, don’t trust it.