I happened to get my US citizenship in June (many, many years ago), so we had a July 4th party a short time afterward. I had already been living in the US for a long time, but still getting citizenship is a big deal.
I agree with this. It is nice for friends to recognize that this is a big deal for the new citizen.
I am wondering about a coffee mug with a US flag on it. A coffee mug might not be a big present, but is something that they could have and use for a long time.