Reel to Reel copy to Disc Help

My Dad back in the day had a reel to reel machine that he used to tape his songs on, my Mom ( 80 years old ) broke my heart yesterday when she said she would like to hear "her" Dad again, he is playing his violin and talking on one of those tapes.
I have six reels that I would like to have copied over to a disk, I am scared to **** thinking I may ruin a tape on a machine that is over 50 years old.

Does any one know a reliable and trusted place where I could this done at.

Thanks
Kenny