Everything really, but here are a few of the highlights I can recall...
A hot air balloon trip over the city - the archipelagic (is that a word?) landscape is made for it. The son of the US ambassador to Sweden was in the balloon with me (his birthday treat) with proper men in black suits and shades security detail waiting at both ends of the trip.
The woodland cemetery:
https://www.visitstockholm.com/o/woodland-cemetery/. Beautiful and peaceful - great if you like chilling out in cemeteries.
The ethnographic museum - striking design and interesting exhibitions. It's also a very pleasant walk from the city centre along one of the watery bits. After visiting the museum, I carried and walking and came to a small modern art gallery showing an exhibition by former-chanteuse, Stina Nordenstam, but I can't
Skansen, the Swedish themed history park, with bonus animals - bit touristy, but interesting and fun.
Pottering around the old city (I stayed in a very pleasant Admiral Nelson-themed hotel there).
Arsing around taking short ferry trips between bits of the city, rather than walking the long way round.
It's just a very good city to walk around - lots of green space and water, traffic is relatively calm. I went in late August or early September - the weather was fine and I had a great time.