A card that isn’t tied to any one hotel, like the Hilton or HYATT cards, is what I would want. Would you suggest a generic, off-brand hotel and travel card?
The Wells Fargo Autograph and Comenity AAA Travel Advantage (both Visa) are your best bets.
Having said that, because you have the Amex Gold card, I recommend looking into other Amex cards that earn Membership Rewards points on travel purchases, even if they have an annual fee. The Amex Green card (3x MR points on travel and transit, $150 annual fee) may be a good option for you.