Day two and I feel like a local already. "We meet again," says the tall black man with the warm brown voice and the small white dog. "Beautiful day." And it is: there's an autumn chill in the air but the sun is sparkling off the water and shafting through the brilliant yellows and reds of the trees. The park is busy with amblers, joggers and dog-walkers like my new friend.
A heron stalks frogs along the reedy edge of the big pond, watched by bobbing ducks. Sheep are baaing, a cow moos and there's even a pleased whicker from a fat, hairy pony as it sees its breakfast coming from the red barn. It feels bucolic - but there beyond the trees are skyscrapers, including the unmistakeable black angles of the John Hancock building, all 60 storeys of it. This is Chicago, and I'm in Lincoln Park.
Reverse the view and from the tower's observation floor the park is a splash of green between the massed roofs of the city's northern suburbs and the vast expanse of Lake Michigan. The reserve's 489ha include beaches, ponds, sports fields, museums, a conservatory, gardens and an outdoor theatre, but most notably there's a free zoo.
That means visits are part of many locals' daily routine, checking on their favourite gorilla or meerkat - or, indeed, cow. As exotic in this city setting as the zebra next door, the cows draw a fascinated audience at milking time in the barn at the Farm-in-a-Zoo.
Not all the animals are official. I watch a young red kangaroo chasing a wild grey squirrel in circles around a tree before the rodent shoots up into the branches. Outside the walls Canadian geese preen themselves on the lawn beside the lake, where waves break on a sandy beach. There's nothing but water right to the horizon, and it's so hard to remember that this is just a lake.
Behind me, ranged along the shore of the South Lagoon, men are focused on catching salmon. There's no finesse here: spawning salmon have no interest in bait, and the method they're using is snagging, using a sort of triple-hook grapple to catch hold of the fish wherever it can. It is a primitive and a high-energy activity requiring constant casting and jerking, and the best thing about it is that everyone is keeping warm, except me, despite the bright sunshine. I duck back into the park through the tunnel under the imposing Ulysses S. Grant memorial with its equestrian statue.
There are 20 statues in the park, including Shakespeare, Goethe and Hans Christian Andersen as well as more local heroes, but the one of the eponymous Lincoln straddles all categories. A bronze standing nearly 4m, it depicts a contemplative and naturalistic Lincoln, his hand on his lapel, about to deliver a speech.
The sculptor, Augustus Saint-Gaudens, had seen Lincoln at his inauguration but also studied the life-mask made a couple of months before the President's assassination, to achieve this faithful likeness.
The mask, and Lincoln's deathbed, are on display inside the Chicago History Museum, just across the lawn from the statue. The museum instils instant guilt in the visitor: there is so much in here it is impossible to give everything its due attention. Part of the problem is Chicago's lively history, which includes several riots, a fire, the Mafia, a World's Fair, Lincoln's rise to power, Prohibition, and a remarkable number of firsts. These range from the world's first Playboy Club (the display complete with bunny costume) to nuclear fission, by way of the skyscraper, department stores, the Pill and Playskool.
It is fascinating and the exhibits are multi-media, absorbing and frequently hands-on - but outside there is even more to discover.
Chicago is a city of neighbourhoods, each with their own character, and Lincoln Park is historical and funky. In the Old Town, trees lay a carpet of yellow leaves over the footpaths and up the steps to the three-storey brick and stone houses that line the narrow streets. They're individual, pretty, decorated with flowerboxes, and there are pumpkins everywhere: Halloween is coming.
At the Fudge Pot, I buy a Toodle (pecans, chocolate and caramel in a delicious splodgy lump). At Woody's Bar, the Bears game on TV is over but the cheerful noise continues, everyone wearing the team colours, knocking back local Goose Island craft beer.
On the corner, young Anetha is looking disconsolate behind her table of cupcakes, $1 each, as more dog-walkers stroll past, smiling but not buying.
Among a diverting mix of shops is a surprising number of comedy theatres, and after dinner in the warm and welcoming comfort of RJ Grunt's - excellent chips and homemade crisps, but you need to be hungry to finish their generous portions of sticky ribs - I go to the most famous.
Second City specialises in sketches and improv and graduates from its stage include John Belushi, Dan Aykroyd, John Candy, Mike Myers, Steve Carell and Tina Fey.
Who knows which of tonight's performers might go on to such fame? It would be hard to pick: the six members of the Apes of Wrath cast are all confident, professional, fast and funny, and nothing the audience throws at them can faze them. From Buzzfeed mockery to a Titanic movie sketch, the laughter flows.
My table seems particularly well-lit, and I discover why when it's time for some audience participation.
Suddenly the spotlight is on me and I'm drawn up onstage to take part in a Wolverine cosplay sketch.
The performers are kind, the audience is generous and, thanks to Goose Island, I don't freeze up. It's all loose and friendly, and part of the Second City vibe.
Afterwards, back at the Lincoln Hotel, it is no surprise to find myself sharing the lift with rock band Bastille. This is Lincoln Park. Anything can happen.
Arrive by air or on the California Zephyr train from San Francisco: amtrak.com/california-zephyr-train
Stay at the quirky and friendly Hotel Lincoln, right across from the park:
Explore with help from Choose Chicago: choosechicago.com
The writer was a guest of Choose Chicago.