It’s been a rough couple of years, and with Sydney opening up again there’s no better time to get out there. If your budget is stretched, that doesn’t mean you can’t have fun. Everything on this list costs a tenner or less – from $1 pizza slices to happy-hour lobster rolls and free outdoor cinemas – so there’s no reason not to enjoy our excellent city this summer.

Farewell a CBD institution with $1 pizza slices
There are only a few months left to eat a slice at Frankie’s Pizza before its Hunter Street site is demolished to make way for a new Metro station. The team is giving it the ultimate last hurrah, with $1 pizza happy hour every single day between 4pm and 6pm. Slide into one of the leather booths with a slice and a pint and listen to the blow-your-eardrums-loud, excellent live music.

Enjoy cocktails or lobster rolls at one of Sydney’s hottest new bars
The new Shell House development is a big-budget experience, but there are ways to enjoy its ground-floor Menzies Bar on a shoestring, if you know what time to arrive. From Monday to Saturday, 4pm to 6pm is Martini hour, with mini versions of the classic cocktail or lobster rolls for $10. If you want both, you’ll need to double the budget, or bring a mate.

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Catch a free exhibition at Carriageworks
Dean Cross’s semi-autobiographical exhibition Icarus, My Son is on at Carriageworks until January 30. Spanning video, sculpture and installation, Cross’s works examine the concepts of home, ambition and loss. The artist uses the father-son dynamic of mythological characters Daedalus and Icarus to explore the experiences of people living in remote communities who want to strike out and see the world.

Eat $1.50 oysters at The Morrison
We love a good cocktail happy hour, but oyster hour takes it one step further. Every Wednesday from 6pm to 7pm, sample some of Australia’s best oysters at The Morrison, including Sydney rock oysters, Pacific oysters, and rock oysters. The menu features sustainable molluscs, sourced from the pristine waters of 20 national park regions across the country.

Tackle an ambitious beachside trail
Nearly everyone has done the Bondi to Coogee walk. That spectacular and very approachable trail is famous with locals and out-of-towners alike. At 80 kilometres long, the Bondi to Manly walk is a more ambitious hike, but the variety of beautiful tracks and coastal views makes it well worth the trip. Take it slow over three days and bring your swimmers for a dip at the start, the finish and along the way.

Learn about food and culture at the AGNSW
The Art Gallery of New South Wales’s free exhibition The Way We Eat examines the human relationship with food through the lens of artworks from China. The exhibition features more than 100 historical and contemporary pieces, plus artefacts related to food and eating. It’s divided into four parts: how food is made, stored and eaten; how culinary tools have evolved; the ways different cultures exchange food; and rituals and food in Chinese culture.

Take a dip in a harbour pool
Whether it’s a rough rockpool fed by the crashing waves of the ocean, or it’s a more sedate, saltwater affair with a good view, Sydneysiders are spoilt for choice when it comes to swimming in harbour pools. Andrew (Boy) Charlton Pool at the edge of The Domain is open until April; $7.05 will buy you a swim and access to one of the most beautiful views in the city, across the harbour to Woolloomooloo. For a bracing dip in a proper ocean pool, try Mahon Pool at Maroubra for free.

Check out a film for free at an outdoor cinema
There are lots of outstanding outdoor cinemas in Sydney – but The Rocks Laneway Cinema makes your choice easy by being free. Set in the quaint heritage square at Atherden Street, the buildings are decorated with festoon lights, and the Harbour Bridge peeks over the top of a sandstone building. What the square lacks in soft grass to sit on, it makes up for with bean bag chairs and deck chairs set up on the cobblestones. Free screenings are every Wednesday night until February 23. Bring a picnic or choose from the myriad nearby eateries, and catch films such as The Holiday, Love Actually and Lethal Weapon.

Do the happy hour rounds all over the city
There are venues doing happy hour every weekday in Sydney. Get tap wine, prosecco or bottled beer for $6 on weekdays at Bopp and Tone in the CBD; $6 pints at Corridor in Newtown on Wednesday, or $7 on Thursday and Friday; and $6 pints, wines and house spirits on weekdays at El Loco at the back of the Excelsior Hotel in Surry Hills, which also does $5 tacos on Tuesdays, or $1 wings on Thursdays.

Drink a sparkling Margarita in the sunshine
Cantina Ok! – home to Sydney’s best Margarita – recently launched a sparkling Margarita, Seltzer Ok!. Made with macerated fresh fruit, including orange peel and lime leaves, mezcal, soda water and a sprinkle of salt (to replicate a salted rim), it’s refreshing with a sour kick. Split a $24 six pack with your mates, and it works out as a very doable $6 per drink. Head to one of these parks on a sunny day and crack one open.