You've already got what some folks consider one of the best travel rewards credit cards on the market. However, a solid airline rewards card with a Visa or MasterCard logo can round out your wallet for those places that don't accept American Express.
Fortunately, with Dallas as your hub city, you've got some excellent options for earning even more rewards points and frequent flier miles when you take to the skies. Consider complementing your Starwood card with perhaps this airline credit card:
Southwest Airlines Rapid Rewards Plus Credit Card. Meanwhile, something else is happening over at Love Field. That's the Dallas home of Southwest Airlines, the disruptive economy carrier that has shaken the industry so hard that rivals like American Airlines and US Airways have considered merging. This airline credit card from Chase offers a flexible rewards program based on Southwest's revamped Rapid Rewards. Southwest's partner network can connect you to more than 800 destinations, opening up even more possibilities for travel.
Like most airline credit cards, this card carries an annual fee. In your case, you'll need to do some math to figure out whether you're getting a better deal by focusing all your spending on the generous Starwood card, or if a basic cash-back credit card will make a better replacement for your Sony Visa.