My humble advice based on your credit score.
1. Citi Simplicity. You have excellent credit. Get the credit line, do a small purchase, pay it, and let it sit. It will also serve you well with its 18month low APR promotions should you slide on some ice down the road.
2. SWA Visa with good bonus (50K with $2k min. spend) for your domestic travel, checking two bags free.
3. TIE UA Mileage Plus with GOOD signup bonus. It was 50K when my DH signed up with $2K min. spend. Check the threads for latest offers. For Rome, Paris, etc. OR
Barclays US MasterCard w/no fee for one year and 30K bonus with first use of the card. For Rome, Paris, etc (w/AA merger, too)
4. AA Citi with 50k bonus. The Citi Simplicity should help get you there (as in approved) with low usage and low debt ratio. More flexibility with your travel visions.
5. Citi HH Signature Visa, the one with 40k bonus for $1k spend in FOUR months. Notice I said four months. Reasonable. No annual fee, either. But, be advised, your APR will be around 15 percent.
I make these recommendations through experience with the exception of the Citi AA which I have never been able to get approved. Best wishes!
PS. Isn't it nuts to have your car paid off seen as a negative? Unreal. Also, I didn't suggest any UR bearing Chase cards. The $200 cashback bonus with the Freedom is now reduced to $100. I don't have experience with Sapphire, etc. Barclays US worked out for me, too