“The sea is as near as we come to another world.”

That quotation glows beneath a giant tank of silvery, circling fish at the Monterey Bay Aquarium.

I look at my kids, standing in awe as a vast bait ball spins above them and see that they’re totally immersed in this ocean otherness.

They are about to go even deeper into the blue.

From our base in Santa Cruz, we’ve driven an hour south, through the patchwork of dunes around Sand City, to reach Monterey.

Entry into the aquarium is not cheap at €35 for adults and €22 for children, but once you get inside, it’s hard to begrudge the cost; there’s just so much to see.

We start with otter feeding, where these sleek creatures are fed shellfish in a variety of complex ‘enrichment’ containers to make dinner a challenge. As part of his humorous commentary, the keeper tells us that they used to serve the otters live shells, but they took to using the glass of their tank to break them open, with predictably poor results for visitors.

The most innovative exhibit by far is the Jellies Experience.

Jaunty electronic music beats at the dark entrance, and the jellyfish dance almost in time, glowing neon or white as they pulse around their tanks.

The kids turn their own bodies into tentacles on a giant screen.

They sketch jellies on a computer and watch their images turn to life, floating up the wall. But the real show, even for little kids, remains the creatures themselves.

Upside-down jellyfish lie on the bottom of one tank, farming algae, while comb jellies shimmer in rainbow colours and purple-striped jellies trail graceful streamers behind them.

We move on to ogle an octopus bigger than my three-year-old, whose sensitive suckers can open jars and caress a trainer.

One floor above, there’s no need for binoculars to admire the wading birds; they are within touching distance on a little beach at eye height.

And in between there’s an ocean-themed dress-up and play area, touch pools crammed with shellfish and seaweed, a parade of puffins and an exhibit about whales aptly named ‘fins, flippers and fun’.

Back in Santa Cruz, the ocean still looms large. This coastal town has a classic seafront; a fairground and rows of shops and cafes sit behind a busy road and a long stretch of seal-coloured sand.

Strangely, the ‘wharf’ (essentially a long, wooden pier) has mostly been turned into a car park and the outlets here have seen distinctly better days.

Jaunty electronic music beats at the dark entrance and the jellyfish dance almost in time, glowing neon or white as they pulse around their tanks

However, when we walk to the end, we are in for a treat.

Sea lions are hauled out on the struts below the pier and holes have been cut into the wooden floor to make viewing easier. Quite how they get themselves out remains a mystery to me, but there they are, sleeping just a metre or so beneath our feet, wedged between beams and buttresses.

Not 50 metres away, an otter swims on its back, clutching mussels that it has wrested from the pillars of the pier.

It vanishes below the water to bash the shells open, then floats again, victorious, prey in hand.

Gulls and cormorants shriek in jealousy and eye my daughter’s bubblegum ice cream as a possible compensation.

Going in for a bite, they fail to reckon with her brother’s vigorous sibling defence and are forced to retreat, sulking. Further down the shoreline, things get wild quickly, as the buildings become sparser and rocky offshore islets appear, crowded with seabirds.

Just 20 minutes inland, we find the Henry Cowell State Park.

California was once covered in vast stands of California redwood trees. They were so widespread that they created their own weather system, keeping the temperature down and generating a hazy fog.

From the mid-1800s onwards, the seemingly limitless supply of redwoods was cut down for construction, firewood and to power limekilns.

It soon turned out that the trees weren’t limitless after all and a forest that once covered more than 8,000 square kilometres of the Californian coast now consists of just a few remnant patches; 96 per cent of the trees were felled in just a few decades.

This park is one of those few stands of intact, unlogged redwood forest left. It’s just spectacular.

After a prowl around the rather excellent visitors’ centre, we set off into the trees. The morning sun is slanting through the distant treetops (these are the tallest organisms on earth, reaching more than 115 metres), illuminating the droplets of mist that hang in the air.

There are 15 miles of hiking trails, through trees up to 1,800 years old, and on our little circular route we see deer, squirrels, insects of all kinds and several über-gooey banana slugs (one gets into my son’s shoe and, when he puts it on without realising, the mess is impressive).

The trees evolved to withstand fire so they heal after a blaze, forming holes in the trunk large enough to fit a troop of children. Ours squeeze delightedly through the kid-sized entrance hole into the pitch-black interior, squealing in semi-feigned terror until a contemptuous older child ruins it by bringing in light from an iPhone.

Fable has it that in 1846, the famous Lt John Fremont camped in this tree while on an expedition to find the shortest route between the Atlantic and Pacific Oceans.

On hearing this rumour, he said: “It makes a good story. Let it stand.”

And so it does. Having worked up an appetite, we head to that most Californian of institutions: a health food store.

Not only are they often affordable enough here to allow you to do a modest weekly shop, they also have delicious deli sections.

New Leaf in nearby Felton does not disappoint, providing us with dhal soup, homemade pretzel bread and a child-friendly chicken noodle soup that is rapidly demolished.

We take home enough for dinner. My fish purchase triggers a long discussion about whether we should be eating the same fish that we had just enjoyed seeing in the aquarium.

My five-year-old’s conclusion? It’s OK as long as it’s caught responsibly. Mission accomplished, Monterey.