If it had been up to me we would have probably visited 10 Unis but my son was reluctant and we went to 3.
2 of the 5 Unis that he put on his UCAS form he had not visited.
The Uni that he will start at next week was one of the two that we did not visit prior to applying and when he put it on his UCAS form it was a last minute decision despite being a top 10 Uni - he actually wanted to go somewhere else, they do change their minds.
I would really encourage your child to visit, I think it helps but remember that there may be all kinds of reasons that they don't want to go to the Open Days - with hindsight I can see that it was anxiety with mine but at the time I really could not see that.
These are huge decisions that they are making and it is scary! Seeing the cities and the Unis is definitely helpful but maybe there is already a particular reason that he has these Unis in mind ie, they are great courses and very good Unis. And maybe that is enough for him, he doesn't need to see them? Has he looked at the course info for them online?
The Open Days were helpful - although there is a lot of information to be gained online and all Unis these day, since Covid, have very good virtual tours etc.
When my son had firmed his choice for this year and it was not a Uni that we had visited, we actually attended a summer Open Day (this June) primarily to see the accommodation because we really felt that we needed to....luckily he really liked it, phew!
Open Days can be full on, loads of people and lots of fairly vocal parents, it can be offputting - I think you need to work out what's important for you to see and just do that.
I would also add that accommodation at Unis these days seems to be a lottery and from everyone who I know who is about to start Uni this month, no one gets their first choice....too many students, not enough accommodation and that is the case at most Unis. We looked at all the campus accommodation but my son was not allocated any of it on Results Day in August, he's in the city....so be prepared to be flexible about it. Campus is better but my son is in city halls which look very nice and are full of first years so I am sure it will be fine.
Know your budget, know your dealbreakers ie, can he share a bathroom, does he want self catering etc? Are there other aspects that the Uni offers that appeal to him - ie, sport, music etc?
Perhaps he could do an Open Day with a friend?
There are lots of way to gain Uni information.
Remember that how we feel and how we'd do it, is very often not how our 17/18 year old children would do it - unfortunately!!
At the end of the day my son will now be attending a Uni that we did not visit initially and that he did not know much about (which I found completely bewildering and slightly scary as did other parents!)....but it has worked out very well, he cannot wait to go and it's an excellent Uni.
Good luck!