Since you get charged the annual fee with the first statement, why not keep it open for 11 months and close it just before your anniversary and the second annual fee charge? Then...use the card for everything you can and rack up some more points. Of course, for that to be a good deal you need to have the discipline to pay off the charges each month so that you're not paying finance charges which can lower/negate the value of any points you earn.
Of course, keep in mind also that on your anniversary date they give bonus points, which some think of as reimbursement for the annual fee. If you hope to do a lot of flying, or prefer to fly standard/business class rather than "wanna fly" class (each class costs different amount of points), then earning those extra points by using the card and paying it off is a wise choice, plus having the account open longer won't ding your credit rating as much (assuming of course, you pay are responsible with your credit card usage).