Tour the historic Alamo (www.thealamo.org), the 1836 site of a furious battle between a handful of independence-seeking Texans (led by Davy Crockett) and a large Mexican army. Today it is a shrine to Texan courage and patriotism.
Become a cowboy
Become a real cowboy on a working ranch holiday in the hill country to the west of San Antonio, near Bandera (www.banderacowboycapital.com), the 'Cowboy Capital of the World'.
Big Bend National Park
See spectacular views of stark desert, forests, mountains and canyons carved by the Rio Grande at Big Bend National Park (www.nps.gov/bibe), south of El Paso. Hiking and rafting, especially in the Santa Elena canyon, are popular.
Buffalo Gap Historic Village
Time warp back to the frontier days at Buffalo Gap Historic Village (www.buffalogap.com), a reconstructed frontier settlement that tracks the history of Indians, buffalo hunters and settlers.
See Dealey Plaza (www.jfk.org), the site of President John F Kennedy's Dallas assassination. There is a dramatic exhibit of the event at the Sixth Floor Museum. The John F Kennedy Memorial at Main and Market Streets is open all year round.
Explore Fair Park (www.fairpark.org), home to the Age of Steam Museum, Dallas Aquarium, the Museum of Natural History (with a superb dinosaur exhibition), the Texas Hall of State and The Women's Museum: An Institute for the Future.
Visit romantic Galveston Island (www.galveston.com), just 40 minutes south of Houston. The island is rich in history and pirate lore and noted for its sandy beaches, fishing, watersports and turn-of-the-century architecture.
Discover the Texas Gulf Coast playground of Padre Island (www.nps.gov/pais), a narrow 170km (95-mile) barrier island with watersports, fishing centres and an impressive expanse of protected National Seashore, wildlife refuges and birdlife sites. It is connected to Corpus Christi by a causeway.
Enjoy fishing, boating and swimming at Highland Lakes, in central Texas (www.highlandlakes.com). Take a wine-tasting trip to award-winning wineries in the surrounding scenic hill country.
Lone Star Flight Museum
Aviation buffs will enjoy a visit to the Lone Star Flight Museum (www.lsfm.org) and Texas Aviation Hall of Fame in Galveston, one of the finest collections of restored aircraft and aviation exhibits in the nation.
Odessa Meteor Crater
View the Odessa Meteor Crater, the second-largest meteor crater in the USA at approximately 168m (550ft) in diameter. It was created when a barrage of meteors crashed to the earth between 20,000 and 30,000 years ago.
Old City Park
Tour the Old City Park (www.oldcitypark.org), a pioneer community in Dallas featuring homes, a church, a schoolhouse and Main Street as it was in the days of the original settlers.
Palo Duro Canyon State Park
Visit Palo Duro Canyon State Park, near Amarillo. The park has dramatic coloured rock formations, is popular for hiking, picnicking, camping and horse riding, and has a rich history of nomadic tribes that hunted mammoth and large game animals.
Ride the glass elevator to the top of the 50-storey Reunion Tower, belonging to the Hyatt Regency Hotel in Dallas. It has observation terraces and a revolving restaurant with nighttime dancing.
San Antonio Missions National Historic Park
Learn about the early efforts of the Spanish to Christianise the native population in southern Texas along the San Antonio River. Tour the four mission churches in San Antonio Missions National Historic Park (www.nps.gov/saan).
Santa Ana National Wildlife Refuge
Go bird watching at the Santa Ana National Wildlife Refuge, and see birds migrating to South and Central America along the Central and Mississippi Flyways.
Go and see the famous Southfork Ranch (www.southforkranch.com), home of the famous TV series' Ewing clan. The ranch is open daily, year-round for guided tours.
Space Center Houston
Explore Space Center Houston (www.spacecenter.org) - the official visitor center of NASA's Johnson Space Center. Climb aboard a computer simulator, touch a moon rock, see a full-size space shuttle replica, see astronauts train for missions, or take a behind-the-scenes tour of NASA.
Take a river walk
Tour San Antonio's Paseo del Rio (Riverwalk) (www.thesanantonioriverwalk.com), a unique shopping and entertainment area that sparkles like a fairyland at night.
West End Historic District
Step into the past in Dallas' West End Historic District (www.dallaswestend.org), a collection of beautifully restored 100-year-old historical buildings turned into museums, shops, restaurants and nightlife.