Grab coffee and simple breakfast at Degraves Street lanes (many cafés open ~7:00am); great for a quick, budget‑friendly start and people‑watching near the Flinders St area.
Easy riverside stroll to orientate the family and see iconic Melbourne architecture — good flat walking for the toddler and free to enjoy; popular and open daily around 6:00am–11:00pm.
Shop fresh produce and ready-to-eat stalls at Queen Victoria Market (open variable hours — typically early morning to mid-afternoon on many days) and picnic nearby; low cost and family‑friendly.
Family‑friendly Italian eateries on Lygon Street offer pasta and pizza; many open until late, but earlier dining around 4–6pm helps toddler routines and budget.
Gentle walk along the riverfront to burn energy before bed — safe, well lit and free; check Melbourne events calendar for any late-night New Year build-up.
Museum is engaging for teens and has child‑friendly exhibits; generally open 10:00am–5:00pm but check any seasonal changes — arrive early for exhibits and to avoid crowds.
Explore stalls and laneway street art before crowds grow; market opening hours vary (some sections closed on public holidays) — check in advance for New Year’s Day closures.
If staying up for midnight, pick a family‑friendly vantage with transport options; otherwise plan a calm evening and settle the toddler for bed before fireworks if possible.
Choose a low‑cost play option in Docklands or the Melbourne Star for views (the latter is ticketed and optional) — check seasonal hours (usually 10:00am–9:00pm).
Quick breakfast and head to the airport for your flight to Hobart or Launceston (flight times vary); double-check baggage and toddler needs before leaving.
Arrive in Hobart and get settled at your accommodation (you said no hotel needed); familiarise yourself with nearby supermarket options for picnic supplies.
World‑class and very different museum — ferry from Hobart Wharf or drive; ticketed and can be stimulating for teens but consider toddler tolerance — check MONA hours (usually 10:00am–5:00pm) and ticket prices.
Catch the vehicular/passenger ferry from Kettering (book ahead in peak season); crossings run frequently but check schedules — total round trip including driving takes a full day.
Do the lookout walk to Wineglass Bay (shorter option to the full hike) — outstanding views, usually open dawn–dusk; bring water, sun protection, and toddler carrier if needed.
Bicheno offers penguin tours (ticketed) — there are free viewing spots at dusk but ticketed tours are more reliable; check times (dusk varies) and consider booking if budget allows.
Gentle boardwalks and lookout points are ideal for families; wildlife is common at dusk — check park notices about required passes or fees before arrival.