Costs run about the national average, though Arizona and New Mexico have their high season in winter, their low in summer.
Weather
Welcome to the land of air-conditioning, especially in cities such as Houston, where the residents and visitors hardly ever venture outdoors in summer, it seems. The air in this part of the world is mostly devoid of humidity, except along Texas' Gulf of Mexico Coast.
Arizona has its best weather between late December and mid April. In summer, it can be around 100 degrees on many days.
New Mexico is similar to its Arizonan sister in weather, the best time in the plains being from December through April, in the mountains in fall and spring.
Oklahoma has some of Texas in its weather, being dry and hot in summer, so come here between November and April.
Texas, vast as it is, has weather that dries you out and beats you up much of the summer, so come here from late October through late April if you can.
Southwest Activities
In Arizona, the sun is king (and cruel master at times), making winter the time to play golf here. You have to get into air-conditioned premises during the hot summer, so visit the galleries and shops (many magnificent of each) in Phoenix, Scottsdale and Tucson then. You can't miss the Grand Canyon (where you can hike, ride a mule or horse, or do many other fine outdoorsy things), and you might like Sedona, especially if you are into New Age stuff. Monument Valley and the Petrified Forest are also highly interesting.
You come to New Mexico to engage Native Americans on their own territory, or maybe to ski, if you come in winter. You can also come to hike the mountains in summer, when they are gorgeous with wildflowers under often crystal-clear skies. Indoors, look for art galleries in places like Santa Fe and Taos, or for small museums telling the stories of the original inhabitants of this part of America, such as the Millicent Rogers Museum in Taos or that town's Pueblo itself.
In Oklahoma, outdoors activities tend to parallel those in Texas, with hunting and fishing the two big sports in each state. Indoors, you should take a look at Native American museums, some on tribal lands.
Texas likes to think of itself as a country (and it was, briefly, back in the 19th century), so there is plenty of room and much to do outdoors. If you don't hanker after horseback riding, joining in dude ranch activities, or playing cowboy around a covered wagon and campfire at dinnertime, you can just go take a hike, wander the Hill Country while hunting for bluebells or even cycle on imaginative trails laid out all across the state. Lovers of indoor things to do can enjoy the several excellent art museums of the big cities (Dallas, Fort Worth, Houston and Austin being the best), or visit monuments such as that at San Jacinto, where the Texians (yes, that's right, the "i" in that word is important to them) beat the Mexicans, or the battleship Texas, moored next door.