Short answer: The Quay is the flat, pushchair-friendly bit and the 40p hand-pulled ferry costs almost nothing and delights small children. The Guildhall indoor family garden is free, warm and dry. Skip the Underground Passages until they are older — there is a crawling section and a strict group size.
The Quay is the obvious base and it earns it. It is flat, pushchairs go everywhere, there is water to look at, and nothing costs anything until you choose it to. Cobbles in a couple of spots will rattle a buggy but there is a smooth route along the whole waterfront.
The hand-pulled ferry across the Exe is the thing to do. It costs 40p, takes about a minute, and it is pulled across on a cable by a person — which for a two-year-old is better than most paid attractions. It runs seasonally and in daylight hours, so check before you build a day around it.
An indoor family garden in the middle of the shopping centre, free to use, where you can bring your own food. The baby change has free nappies, which is the sort of detail you only appreciate when you need it. It is the single most useful wet-weather stop in the city with a toddler.
The oldest public sensory garden in the country, free, and next to a play park — so it covers both the calm half hour and the running-about half hour. It is a walk out from the centre rather than in it.
iPlay is the soft play answer. Sessions are two hours and include time to eat, the sensory room is genuinely good rather than a cupboard with lights in it, and it is reasonably priced for what it is. On a wet February afternoon it is worth every penny.
The Prospect Inn sits right on the quayside, is very dog friendly and has space outside to let a child move. It is closed on Mondays. Istanbul Restaurant is open 11am to 11pm every day and brings free breads and dips out quickly, which buys you the first ten minutes you need.
Park and ride beats driving into the centre and it is cheaper, but with a toddler the bus adds a leg at each end. If you are coming for the Quay specifically, the Quay car parks put you right at it. Exeter is a city, so the centre is busier and noisier than the coastal towns — the Quay is where it calms down.
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