Sounds like the OP does not want to spend much on the card, so bonus categories are not relevant. Truthfully, having a rewards card to NOT use it does not make much sense to me. Anyway...

Do not close your existing card. Call and ask to downgrade to a no annual fee card and buy a cup of coffee every six months to keep it alive. Your credit score will thank you.

Amex Offers often have good rebates, but are often targeted. Check the thread in the Amex forum to see if there are any that you would be interested in. I think my most profitable were the $20 back on $100 at Walmart/Target (several times per card) that got used for gift cards for places I actually shop at. There are a few no annual fee cards that would work including a Hilton card that would let you double dip.

Chase IHG is worth keeping if you can use at least one free night a year. I also keep the Club Carlson card post devaluation since the 40K points a year end up getting used for a slight profit eventually - fewer hotels to redeem than IHG though.