If your end game is just to be able to hear the audio at the correct speed in which it was recorded, you could simply record the audio into a DAW and then fix the speed digitally. Simple as pie!

If I were to use a DAW to do as suggested and I also want to take some of these tapes and make some CDs with them which DAW do you suggest I use. I have no experience at all with a DAW and my needs do not exceed what I've just mentioned.

You need a way of changing tempo and pitch together. Most DAWs go out of their way to separate these two. The simplest DAW that will do this job is Audacity. It's free to download.

Assuming you have a way of connecting your tape machine to your computer, you would need to select the correct input device in Audacity, hit the red Record button and then play the (double-speed) tape from the start.

At the end, hit Stop, then select the entire recorded file as though it were one song. In the Audacity Effects menu, there is a Change Speed option. You would need to select 0.5 as the required speed multiplier. This may take a few minutes, depending on the length of the tape. Export the resulting track as a file.

This is the relevant page from the Audacity help file:

https://manual.auda…

Excellent info from Bos.

If any of this becomes too daunting for you, you could also hire a local recording studio. It shouldn't cost very much as its a simple part of audio restoration most studios can do. They would also be able to transfer the audio other formats like CD or wav, mp3 etc for you.

You also need an audio interface to do the transfer. 

Thank you for the info. I'm now using audacity where i divitally copy the tape, halve the speed and when playing it back re-record the digital to analog. For the one original tape i now get two tapes (7" reels). It takes some time but now i have easy access to any particular sing i may choose.

Well done - I'm glad you got that working. You now have experience of simple DAW operation!

I hope you kept the reduced-speed files, since you can use Audacity to export them as .MP3s to a more suitable storage medium. This could include a USB memory stick, a CD as data (not audio) or somewhere in the Cloud.

The original 1.875ips tape tracks were probably mono and not particularly hi-fi quality, so storing them efficiently as mono MP3s will not noticeably reduce their appeal.