This is pretty much a one-street town; just about everything in Springdale is aligned along the main street, UT-9. Everything is fairly close together, often making it pretty easy to walk around town. Bicycling is also a good way to get around town or into Zion.
By Shuttle
As part of Zion National Park's free shuttle system, Springdale has a route running through the town April-October. Parking at the Visitor Center in Zion often fills up, so if you're spending the night in Springdale you would do good to leave the car at the hotel and take the shuttle into the park.
The route has 9 stops, with three of those available only on request or when people are waiting: Majestic View, Silver Bear request only, Driftwood, Bit & Spur / Zion Park Inn, Pizza & Noodle / Bumbleberry / Zions Bank, Canyon Ranch / Desert Pearl / Post Office request only, Flanigans / Kimaries, Watchman Cafe / Cliffrose request only, and the Zion Canyon Theater. The last stop is within easy walking distance of the Park Entrance and the Zion Visitor Center.
In spring and fall, the shuttle runs from 6:30 AM until 10:15 PM, with 10-15 minute frequency. In the summer mid-May to early September, the shuttle runs from 5:30 AM until 11:15 PM, with 10-15 minute frequency, and 20 or 30 minute frequency in the very early morning and late evening.