Houstonians John and Dominique de Menil amassed an astonishing stockpile of 10,000 objects spanning everything from prehistory to pop art during their lifetimes and this assortment has been almost doubled since then to form today’s transfixing body of work housed in the Menil Collection, a long, white modernist building designed by Renzo Piano.

The best free romantic thing to do in Houston awaits in Hermann Park. This vast and varied verdant expanse is not just a pretty face flanked by blockbuster museums: it has its own cultural shenanigans going on, including this amphitheater designed by William Ward Watkin who had a hand in many of the metropolis’ most magnificent structures. After a day spent exploring Hermann Park, a genteel conclusion is to recline on the grassy slopes of the theater enjoying a free concert or play.

The lion’s share of the city's success stems from the Port of Houston which, through this channel, is able to be the most commercially successful port in the USA and the sixth-largest anywhere in the world. The free, 90-minute pretty-but-gritty tours along the waterway might be the best-kept secret on the long list of city attractions: they are incredibly informative, yield sensational panoramas of the Houston cityscape and even come with complimentary refreshments.

The de Menils commissioned this unusual contemplative space in 1964, aiming to create a nondenominational place of worship. The chapel was the building that fabled American abstract painter Mark Rothko spent the final years of his life working on. Walls within the octagonal structure are adorned in 14 Rothko canvases. At first, these appear black but, the longer you focus, they morph as if by magic into myriad different shades: a profound experience for a profound place.

Focussing only on art created in the last 40 years, the Museum District’s Contemporary Arts Museum is a centre for ever-changing displays of cutting-edge works and exhibitions by the likes of Robert Rauschenberg, Nic Nicosia and James Turrell. There is no permanent collection here, but this ensures repeat visits invariably offer something utterly different and thrilling. It sits across the street from the equally free Lillie and Hugh Roy Cullen Sculpture Garden, a serene green enclave.

The Shri Swaminarayan Mandir was the first Hindu Mandir (temple built to sacred designs laid down in ancient scriptures) of its kind in North America and makes a truly splendid addition to a city renowned for raising and changing the game with its architectural innovation. Come to gaze in awe – or to worship – cost-free, and reserve time for a turn around the arresting 22-acre grounds. The temple is out in Stafford, 20 miles southwest of Downtown.

After Abraham Lincoln’s abolition of slavery, and word reaching Texas that slaves had been emancipated on June 19, 1865, black communities countrywide began to celebrate the anniversary (as Juneteenth). Galveston, just down the road from Houston, was the first city to do this. But in Houston former slaves went to greater lengths. They purchased these 10 acres of land in South Central Houston as a special spot for Juneteenth festivities, which still happen here today.

Just as Austin has Congress Avenue Bridge for bat-watching, so Houston has Waugh Drive Bridge. An estimated 250,000 Mexican free-tailed bats reside on the underside of this bridge across the Buffalo Bayou, and differ from Texas’ other big bat colonies in living here permanently, rather than migrating south in winter. Come sunset, they launch in huge cacophonous crowds on a nightly insect-hunting spree. Behold the spectacle from the bridge or the park pathways below.

Houston’s favourite alt event is the Art Car Parade, where wackily decked-out autos and indeed a cornucopia of other eccentric wheel-mounted art takes to the streets in what is, this being Texas, the biggest event of its kind in the world. The Art Car Museum, on Heights Blvd south of Katy Fwy, is where you get to see a few of the fabulous contraptions that won, complimentarily. The museum’s nickname – the Garage Mahal – gives a clue as to the overarching theme.