Each day below stays in one part of town, and each one carries a swap for the afternoon when the weather turns. Check the day's opening hours before you leave the hotel, since the tower, the aquarium, and the science museum all keep seasonal hours that catch people out.
Day 1: The Old City on Foot
Start at the Central Market, one of Europe's largest and oldest food markets, for breakfast under the glass dome and iron frame. The market runs from seven in the morning to three in the afternoon, Monday to Saturday, so breakfast there means going early. From there it is a short walk to the cathedral on Plaça de la Reina, where €9 buys entry and a look at the agate cup in the Chapel of the Holy Chalice that many scholars treat as the strongest candidate for the Holy Grail.
Climb El Miguelete next door, the octagonal bell tower that rises 51 m, roughly sixteen stories, for €3 and a rooftop view across the old town. After lunch, walk a block to La Lonja de la Seda, the silk exchange built between 1482 and 1533 and listed by UNESCO. Entry costs €2 and is free on Sundays and public holidays. Spend the afternoon in the lanes of El Carme, and finish at one of the medieval gates: Torres de Quart or Torres de Serranos, €2 each, both with a view from the top.
Evening belongs to Ruzafa, south of the center, a neighborhood that began as a ninth-century Moorish garden and now holds one of the city's tightest clusters of restaurants. Walk in around nine, or book ahead if it is a Friday or Saturday.
When it rains, trade the tower and the gates for the Almoina crypt behind the cathedral, an underground museum of Roman and Moorish remains for €2, then the Silk Museum on Carrer de l'Hospital for €6.

Day 2: The City of Arts and Sciences, Then Sand
Go to the Oceanogràfic first thing. It is the largest aquarium in Europe, split into seven zones, with a dolphinarium and a walk-through shark tunnel, and the building itself is a water-lily shape designed by Félix Candela. A morning covers the highlights; families with children should plan on the whole day. Buy the combined ticket if you will visit two or more buildings, since it stays valid for three days.
Have lunch near the complex, then walk the rest of it, which costs nothing and lets you view the buildings from the outside. The botanic garden at L'Umbracle is free too, and the sculpture walk through it is short enough to fit before lunch. Take the metro or a bike down to Playa de las Arenas after that and follow the promenade north, where the bars and ice cream shops start.

Paella is the meal to plan around today, so keep the middle of the day free for it.
For rain, swap the beach for the science museum at €9.40, where three floors of hands-on exhibits sit inside a building shaped like a whale skeleton, and catch a film in the Hemisfèric cinema instead of the sunset.
Day 3: The Lagoon and the Riverbed
The Albufera sits 10 km south of the city, about six miles, a freshwater lagoon ringed by rice paddies and the place paella comes from. A traditional boat ride across the water, a walk along the fields, and lunch in El Palmar village fill a morning and the early afternoon. Going with someone who knows the boat operators saves you the guesswork, and a Valencia tour that includes the transfer turns it into an easy half-day.
Back in the city, rent a bike and ride the Turia Gardens from the old town to the City of Arts and Sciences. The river was diverted south after the 1957 flood, and the empty bed became a park that runs the length of the city, flat the whole way and lined with orange trees.
End with horchata and a fartón, the small pastry made for dipping, at Horchatería Santa Catalina by the market, or an Agua de Valencia, the orange juice and cava mix invented here in 1959. It is stronger than it tastes, so order one and see how you feel.
Rain on day three means Bioparc Valencia, where African animals live in open enclosures and the lemur house lets you walk through, for €28.90 to €31.90, or the Museum of Fine Arts, which is free and holds two thousand pieces.