From the city you can walk until the Sofiero castle...it's a long but beautiful walk. You'll see the ocean, rich houses and nice gardens.
When u get to the castle, make sure u'll visit the entire garden...it's so magic!!!
I didn't get into the castle...but it's wonderful anyway...
I have to say I was slightly disappointed by Sofiero. Its gardens (rather than the castle itself) is what people come for and they are fantastic but not that fantastic compared to some other Swedish gardens (my own favourite is the Botanical Gardens in Göteborg). At SEK 75 a person, the entrance fee seemed a bit steep for what you get. However, the rhododendron in late May and early June spreads its way down the slopes towards the strait in all colours you might want, and later in summer you can admire the rose garden. There is also a sculpture area, a totem pole and a hothouse, as well as opportunities to buy seed for your own garden.
The quite plain castle was built for Sofia of Nassau, a German princess who married our king Oscar II, hence its name. It has an outrageously expensive and good restaurant and if that's out of you budget, you can have a picnic or ice cream in the gardens where there is also a playground. The orangerie is the place for various exhibitions on "kitchen herbs", "spices", "fruit" and similar. Sofiero also hosts concerts both classical and Swedish pop, a couple of times in summer, as well as the odd dog show. See more in my travelogue if this seems tempting.
Built where the sound is narrowest, the palace Sofiero overlooks a colorful garden with lots and lots of rhododendrons. When I visited Helsingborg, it was raining cats and dogs, so I didn't really want to walk soaking wet in the Sofiero garden. Hopefully I'll soon have a chance to visit Helsingborg again and then I promise to get back to you with more info and some nice photos.