Only four as well as a half blocks, I thought. No need to use my weeklong bus and cable automobile pass ($26). But within a block, the downpour had rolled off my waterproof jacket and soaked my jeans through. On the next block, a homeless woman joined us, complaining that “it’s a dreadful thing when you must steal cupcakes to eat.” True , but I was stressed to commiserate. And on the third block, the inevitable happened. The paper grocery bag hanging over the back of Sasha’s stroller disintegrated in the rain, spilling a week’s worth of organic food — a dense honeydew melon, supple young broccoli, small cremini mushrooms — across the flooded sidewalk.

DAY after day in January, the rain poured down on the Los angeles coast without pause or pity — a number of the worst storms to hit the state in a decade. High winds took out power lines and overturned SUVs. Garbage washed up on beaches. Hundreds of people were evacuated from their mudslide-threatened homes. And on two particular Tuesday afternoon, in the Mission District of San Francisco, the heavens focused their fury on a visiting brother from Brooklyn — i.e., me — who, so self-absorbed he was blind to the calamities around him, had decided to walk home from the supermarket with his 13-month-old daughter, Sasha, in her stroller.

Defeated, I screamed words that young Sasha probably should not have heard. This was not how the week was supposed to go. With her brother in Berlin on a business trip, Sasha and I had flown here for a small low-budget, daddy-daughter bonding time. Ambitious? Perhaps. But in her brief life span, Sasha had already proven herself a hardy voyager, with four overseas trips under her belt. He also had flying down to an art, sleeping very from takeoff to landing, with not very a squeal in between. This trip was a chance to demonstrate my talents not only as a frugal traveler but as a self-sufficient, all-in-one SuperDad! I would feed, dress, neat and entertain my small girl for an entire week, while exploring a strange city on the other side of the country — and doing so, of coursework, without spending a lot of money.

At first glance, San Francisco would appear to be precisely the wrong place to do this. According to Forbes magazine’s 2009 survey of America’s most pricey cities, San Francisco ranks fourth, and according to 2008 Census figures, San Franciscans have fewer children than the rest of the state. The hills are rough on strollers, and the homeless people, strip clubs and ubiquitous pot smoke can challenge a protective parent’s patience. Do the math, and it looks crazy to take a child there for holiday.

On that front, that rainy Tuesday was actually going well. Sasha’s stroller was sturdy and lightweight, the cheapest in the Maclaren line and ideal for travel, and its transparent rain fly was keeping her warm and dry. Those food bobbing in the water had been a bargain, , despite the fact that they’d come from the Rainbow Grocery, a coop that composts, shuts down for both César Chávez Day and Gay Pride Day and is, generally, pricey. Except on Tuesdays, Wednesdays and Thursdays, when you can deploy a coveted coupon, found in the local phone book, to knock 20 percent off your bill. (Mine came to $26.95.)

But child vacations involve a complicated calculus. For two thing, at over a year elderly, Sasha isn’t exactly a sophisticated traveler. All he wants is to run around and see new things — whether on the street or at an art gallery — which meant that, for the most part, they could go wherever I wanted. And although San Franciscans may not be the most family-oriented, those who do have children form fierce, tightly knit communities centered on schools, playgrounds and the Net, which I hoped to tap in to. The, uh, colorful street life, meanwhile, would not very intrude on a 1-year-old’s consciousness; no awkward explanations necessary. And as for the expense, well, I knew I’d find ways around that.

And when they finally soldiered home — after I’d taken a deep breath, found the reusable grocery bag I’d hidden in Sasha’s diaper bag and gathered up our food — it was not to a cheap hotel but to a stunning Victorian house for which they were paying $90 a night. I’d found the place through AirBnB.com, a Web-site that lets people rent out their futons, spare rooms and entire apartments to travelers like myself; it’s a cross between Craigslist, CouchSurfing and VRBO.com. In fact, I never even looked for a hotel at all. Why spend more for less room, a hip lounge as well as a fitness center? Travelling with a young kid brings new requirements: a kitchen where I could make Sasha cheap, healthful meals; a spacious bathroom where I could bathe her; free access to laundry machines; and plenty of space to run.