Melbourne's headline attractions are mostly free and mostly a short tram ride from Flinders Street, which means the budget goes on the sport, the food and the day trips instead.
NGV International
The larger of the two National Gallery of Victoria sites, at 180 St Kilda Road just over Princes Bridge, open daily 10am–5pm with free general entry and charges only for ticketed exhibitions. The Australian collection, Indigenous and non-Indigenous, is at the Ian Potter Centre in Fed Square — also free, also 10am–5pm.
Queen Victoria Market
Trading since 1878 on the northern edge of the CBD: Tuesday, Thursday and Friday 6am–3pm, Saturday 6am–4pm and Sunday 9am–4pm, closed Monday and Wednesday. Specialty shops only open at 9am, so an early arrival gets you the deli and produce sheds rather than the souvenir aisles.
Royal Botanic Gardens Melbourne
Thirty-eight hectares off Birdwood Avenue, free and open daily 7.30am–5.30pm with the visitor centre 9.30am–5pm. More than 8,500 plant species, an ornamental lake you can punt on, and the historic Melbourne Observatory. The paid Aboriginal Heritage Walk, led by First Peoples guides, is the one worth booking ahead.
MCG tour and the Australian Sports Museum
The museum sits under the stands at the MCG and guided tours go behind the scenes of the ground itself, with premium and themed options including AFL and American sporting history, plus a tour-and-lunch package in the Committee Room. Both are booked through the museum's own ticketing site, and match-day ticketholders get separate pricing.
State Library Victoria
Open daily 10am–6pm on Swanston Street, free to walk into, and closed only on New Year's Day, Good Friday, Christmas Day and Boxing Day. The Ian Potter Queen's Hall keeps shorter hours, 10am–4pm, and the Cowen Gallery follows library hours except during events; parts of the Dome are periodically closed for works.