I did have the Household bank credit card, one of the first cards aftr BK. If you close it it will remain on our report for an indefinite period of time. However after ten years or so it will drop off. Depending on when you established additional credit after this yu ay take a small hit when it falls off. But as long as you have good credit reporting it will be negligible.
I have a freind that was ten years between closing an account an reopening a new onw. In that case when the oldest account fell off it was an 80 point drop.
I do not believe in keep cards with annual fees unless that's all you can get. They are designed to establish xcredit and when you are approved for better offers, they have done their jobs IMHO