Klubbensborg Camping

auto-translated: Great campsite if you are traveling with dogs and visiting Stockholm. Lots of great opportunities to walk your dog, even with bathing rings directly from the site. You can be in the city in 30 minutes by bike.
Staff friendly, sanitary ok, could actually be a bit more frequent

auto-translated: Klubbensborg Camping is a practical choice for us: about 40 minutes of cycling and then you're in the heart of Stockholm. Camping itself is not great, sanitary facilities are adequate but when there are a lot of people they get dirty quickly. Although they have done their best in recent years and refurbished the kitchenette and toilet/showers behind it.
If you don't have bikes, you can take the metro (15-minute walk), which also takes you into the heart of Stockholm.
Stockholm itself remains a fun city to visit, especially when the Kulturfestival (mid-August) is held.

auto-translated: Good city campsite, so obviously a bit more crowded. Most campers come here to visit Stockholm. The tent site is small and very shaded. The latter is fine in warm weather, but it remains very wet in lesser weather. Sanitary facilities are outdated, but clean and sufficient. Do take your chances when it says at the entrance that the campsite is full and when the phone is not answered.