I headed a few blocks to Rodeo Drive, pausing to window-shop at Porsche Design, Harry Winston Jewelers and Bijan. The stores were not yet open — not that it really mattered; they’re not exactly frugal territory. Sweaty and clad in just a T-shirt and tight biking shorts, I’m not sure I would have been welcome anyway.

I worked my way through some small side streets over to a place that would sell goods I could actually afford: the Beverly Hills Farmers’ Market. It was the first of many frugal food destinations recommended to me by friends and colleagues. (As I would learn during my trip, the incredibly varied cuisine of Los Angeles is a frugal traveler’s dream, as long as you don’t mind buying from stands and trucks.) One good thing about a traffic-clogged city is that there are plenty of signs to lock your bike to. After doing just that, I wandered the market, where I fueled up on fresh grapefruit juice, Mexican chilaquiles and British scones for just over $10.

My brunch over, I could embark on my entertainment for the day: a tour of stars’ homes. Instead of paying $40 to take a tour in one of those open-topped vehicles, though, I set off on my own version of the tour, using as source material the bike route laid out in the “Beverly Hills Star Home Loop” section of the book “Bicycling Los Angeles County” by Patrick Brady (Menasha Ridge Press). Though the book overall proved useful, this particular tour was plagued with errors, telling me to turn left when I should have turned right. It did guide me to houses once inhabited by George Burns, Frank Sinatra and the Menendez brothers. Judging from the hedges hiding it, the Sinatra house was probably extravagant, but the other houses hardly looked more outrageous than those of any other upscale suburb. It was the broad, empty streets, the Maseratis in the driveways and the utterly impeccable landscaping that suggested something different. Well, that and the star-tour vehicles that crawled past me, their passengers staring my way as if I could have been a star myself.

From there, I cruised a few smooth miles east toward Hollywood via back streets parallel to major thoroughfares, where, even on a Sunday afternoon, traffic was looking like a challenge. (A smartphone with Google Maps or other GPS-like applications is an invaluable help, although I believe they still make maps on paper as well.) Once there, I made a turn on Vine for a quick stop at the Cactus taco stand, recommended by a college friend, for three tacos, one each of carnitas, moist goat and spicy al pastor. And then I was off to gawk at Jack Nicholson’s footprints outside Grauman’s Chinese Theater, in the middle of a crowded retail strip a couple of miles north of the taqueria — and a lifetime away from the calm residential streets I’d navigated in Beverly Hills that morning. My final stop that evening was at Jitlada, a foodie-anointed Thai restaurant a few more miles east of Grauman’s. I stuffed myself with the Crispy Morning Glory Salad and the pork kua kling, ordered in its second-most spicy version (which I would characterize as “blazing inferno”).

Thoroughly decongested but exhausted, I performed a routine that became easier as the week progressed: I waited for a bus, then when it arrived, I caught the bus driver’s eye, lowered the bike rack on the front of the bus, and fastened my bike into place. Then I boarded, resting my legs on the ride back to my bunk.

The Coast

It would be crazy to try to see the 15-mile coastline between Santa Monica and Redondo Beach on anything but a bike. It’s flat and almost entirely traversable if you use the dedicated bike paths that run along the beach. You can turn back any time you want, and you can go any day of the week at any time, since you won’t have to compete with rush hour (or even weekday) traffic.

By bicycle, it was an easy trip. I was joined by Jeff Hartleroad, an old college roommate — now a neonatologist — whom I hadn’t seen in well over a decade. Jeff is a serious biker. I was temporarily intimidated by the fact that he was wearing shoes that actually clipped into the pedals, but I got over it.