Austin

Built in 1888 of red granite, its dome tops out higher than the US Capitol in Washington. Guided tours are free, and from the rotunda floor you look up at a star set in the dome's eye. Bags are screened at the entrance.

In summer over a million Mexican freetail bats roost in the concrete crevices under the bridge. From March to October they pour out together at dusk and scatter east to feed, watched from the bridge pavement and the lawn by the water.

Water welling up in Zilker Park is dammed into an outdoor pool that holds near 20C year-round. The bottom is gravel and rock, not concrete, and slick with algae; on Thursdays it shuts by day for cleaning. An endangered salamander lives only in these waters.

The dammed Colorado River forms the lake, ringed by a walking and cycling trail of about 16km. Kayaks and paddleboards can be rented, but swimming is banned. The name honours Lady Bird Johnson, the president's wife who championed the trail.

South of the river, Congress Avenue is lined with boot shops, vintage clothing and food trucks. Looking north up the street, the Capitol dome sits dead ahead. A line scrawled on a cafe wall, i love you so much, has become the photo stop.

Live music bars crowd this east-west street downtown, and on weekend nights it closes to cars. The eastern blocks pack in a young party crowd, while the western blocks and nearby Red River Street lean towards rooms built around the bands.

A presidential library on the University of Texas campus, where the archive, filed in red boxes, is shown floor upon floor behind glass. The top floor holds a slightly scaled-down copy of the Oval Office.

A limestone hill west of downtown above a bend in the Colorado River. Stone steps from the road reach the top in minutes, so crowds come at sunset to watch far-bank mansions and the bridge turn red. Parking is tight, and on weekend evenings the roadside fills.

A round pool formed when the roof of an underground river caved in, with a waterfall spilling off the overhang that remains. The drive west takes close to an hour, and entry needs booking. On days when bacteria counts run high, swimming is off.

Texas history north of the Capitol, centred on the reassembled hull of La Belle, the ship of the French explorer La Salle that sank in the 17th century. A giant star sculpture stands on the entrance plaza.

The University of Texas art museum, whose grounds gained Austin in 2018, the only building Ellsworth Kelly designed. Step into the white stone chapel and light through coloured glass pools across the floor like a rainbow. Colours peak on a bright afternoon.

A garden of Texas native plants founded by Lady Bird Johnson and now run by the University of Texas. In March and April the state flower, the bluebonnet, turns the slopes blue. Climb the stone tower to look over the garden and Hill Country grassland.

Just past two hours' drive west rises a pink granite dome, its summit about a 30-minute climb up steep bare rock. The name comes from legends of the rock groaning as it cools at night. Weekends hit capacity, so reserve a day pass ahead.

West of Austin, roughly an hour away, the Pedernales spills over tilted tiers of limestone. No swimming at the falls; a sandbar downstream has its own swim zone. Upstream rain can raise the river within minutes, so head uphill at any warning.