Be guided by your son, which sounds like what you plan to do anyway. In my case, my children asked me to attended their first one with them and then chose to do the rest themselves. They felt they owned the process and said staff and students were more attentive precisely because they were in a minority of solo attendees.
To pick up on observations by other posters:
It is possible to discuss uni options meaningfully with children without attending Open Days. There is info on the web that can be reviewed together; you can visit locations at other times with them; I did that in some cases after an Open Day with my child acting as the guide.
Obviously it can be helpful to have an extra pair of eyes and ears and an on-site sounding board. However, my children did a lot of prep before each Open Day to mitigate this. It also meant the onus was on them to 'lock on', really use their limited time wisely and ask questions.
In terms of long distance travel, Edinburgh in your case, could your son consider very early morning trains and accept they miss the morning sessions? Domestic flights might be an option.
To conclude, many DC much prefer their parents to accompany and, if that works for them, support them but equally, if they want to go solo, run with it.