With its vertical hills and busy traffic, Sydney doesn’t instantly appear to be the most bike-friendly of cities. But with the extension of bike lanes and a growing awareness among drivers, cycling has become an easier and more appealing activity for even the most fair-weather of riders. There's a certain freedom that comes with riding a bike. Faster than walking and more mobile than a car, it’s both efficient and exhilarating. From the elevation of your bike seat you feel a part of the worlds inhabited by both pedestrians and traffic. There is no set route, few rules and you can stop whenever you want – all of which make the bike the perfect vehicle for a Saturday of gallery hopping across the city’s inner suburbs.

Below is a suggested route, from Eveleigh to Paddington. It takes the better part of a day but can be done in sections or used as the bones for a more comprehensive art adventure. The activities and opening hours are based around a Saturday, so double-check opening times before you head out on any other day.

Start: Muscle your way through the throng of canvas bag-carrying shoppers and their entourage of kids and dogs, and begin with some breakfast at Eveleigh Farmers Market (243 Wilson Street, Eveleigh, 8am–1pm). Fill up on samples or cobble together a piecemeal breakfast from the various stalls before heading across the disused rail lines to Carriageworks (245 Wilson Street, Eveleigh, 10am–6pm). Carriageworks is a multi-arts centre in the heritage-listed old Eveleigh Rail Yards. The foyer is often used for visual art exhibitions, but the building itself is worth a look inside. Who knows what else you will find going on: talks, a performance, nude live art perhaps? If you’ve slept in then you might just catch the tail end of the market and arrive in time for the opening of Anna Schwartz Gallery (245 Wilson Street, Eveleigh, 1pm–5pm) next door. The Sydney branch of this Melbourne-based gallery is an enormous space, dealing with work by established Australian and international artists, along with the occasional curated group show.

Hop back on your bike and cruise down Abercrombie Street to The Commercial (148 Abercrombie Street Redfern, 11am–6pm), a garage-sized new edition to Sydney’s gallery scene, focusing on the work of emerging artists. Three doors up from the gallery is The Town Bike Pitstop and Redfern Bike Depot (156 Abercrombie Street, Redfern, 8am–4pm). Here you can borrow some tools if your bike needs servicing, or pop in for a coffee if you’re in need of some refuelling yourself.

Further down Abercrombie Street, across the Cleveland Street divide, are neighbouring galleries MOP Projects (2/39 Abercrombie Street, Chippendale, 11.30am–5.30pm) and Galerie pompom (2/39 Abercrombie Street, Chippendale, 1pm–6pm). Artist-run initiative (ARI) MOP Projects has been open in Chippendale since 2003 and must have seen a few changes to the area in its time. The gallery program is an ever-evolving calendar of exhibitions, curated by a volunteer committee. Earlier this year, Galerie pompom opened its doors as the commercial companion to MOP Projects, developing a healthy stable of young Sydney-based artists.

En route to White Rabbit Gallery (30 Balfour Street, Chippendale, 10am–6pm), duck up O’Conner Street and peer over into the Central Park development of the old Kent Brewery. Brook Andrew, Mikala Dwyer and Caroline Rothwell are the three artists whose work can be seen sprouting from the building and in the grounds as part of a temporary public art project on the site.

White Rabbit Gallery is home to the exceptional private collection of Chinese contemporary art amassed by the Neilson family, focusing on work produced since 2000. Spread over four floors of a former car showroom, the collection is re-hung biannually. There is always something wacky, enticing or unexpected. Best of all is the downstairs tearoom, which is the perfect pit stop for some tea and dumplings when the art-fatigue and hunger are beginning to tighten their grip.

Leaving Redfern and Chippendale behind you, career your way through Prince Alfred Park to Surry Hills’ Firstdraft Gallery (116-118 Chalmers Street, Surry Hills, noon–6pm). Firstdraft has been at the heart of Sydney’s ARI community since its inception in 1985 and continues to deliver a constant rotation of exhibitions of work by emerging artists, as well as offering artist residency programs and opportunities for young curators and arts writers.

Until now, it’s been a fairly easy ride. For your first leg-burning hill, head down Elizabeth Street and up Cooper Street to Chalk Horse (8 Lacey Street, Surry Hills, noon–6pm). The neon sign above the gallery gives the inconspicuous space away, as do the swarm of people milling in the street if an opening is on. It might look dark inside, but pop your head around the door and you’ll find Chalk Horse to be a welcoming little space. Try to get a sneak peek at the artist’s studios out the back if you can.

Zigzag your way through Surry Hills towards Oxford Street in Paddington. If you’re passing down leafy Napier Street then pop into the College of Fine Arts’ Kudos Gallery (6 Napier Street, Paddington, 11am–4pm). From Oxford Street take a left down Glenmore Road and then left again at Five Ways to arrive at Sherman Contemporary Art Foundation (SCAF) (16–20 Goodhope Street, Paddington, 11am–5pm). Previously Sherman Galleries, SCAF is now a not-for-profit organisation working with artists from Australia, the Asia Pacific and the Middle East to commission new work and develop a versatile free program of discussions, film-screenings, forums and floor talks. If you’re in need of some peace and tranquillity at this stage, head out to the Zen garden for a breather.

Roslyn Oxley9 Gallery (8 Soudan Lane, Paddington, 11am–6pm) is last on the list, and the good news is that it’s a coast downhill from here. Catch your breath there for a while with an exhibition program focusing on contemporary artists from Australia and the Asia Pacific region.

End: There is no way out of the belly of Paddington other than head back up hill again (we’re sorry). Cascade Street might just break you (you can be forgiven for getting off and walking at this point) but the beer at the Four in Hand Hotel will be worth it in the end. If you’re hungry, try to get to the bar before 4pm or after 5.30pm on a Saturday, as the kitchen is closed for a break at this time. Pull up a stool and while away a few hours, resting replete in the knowledge that both your eyes and your thighs have had a good day’s work-out.

For a complete and printable map including all the venues listed above, see here