@Marie5656 - I recommend keeping the credit card account open. Just pay it down month to month, like you said. And it's always a good idea to pay at least 10 or 20 bucks over the minimum if you can. My payments are set up as Auto-Pay through my bank, so I don't have to send a check, I just mentally deduct the payment amount from my monthly balance and always I know how much is in my account.
Anyway, I'd keep the account open. Just keep making the payments but don't use the card, at least not until the minimum payments come down to double digits.