Nottigham or Exeter for Law?

According to The Complete University Guide, average entry grades for Law are higher at Nottingham than Exeter so don't let the offer fool you that Exeter is better or harder to get in to. Exeter might still have accepted you if you achieve 32 (or less).
Pro of Nottingham - more history to the university. Nottingham University is well known in Law circles.
Pro of Exeter - if this counts as a pro to you - more students who went to private school. But, since much of the Exeter campus looks quite modern, it might not 'feel' particularly private school.

According to The Complete University Guide, average entry grades for Law are higher at Nottingham than Exeter so don't let the offer fool you that Exeter is better or harder to get in to. Exeter might still have accepted you if you achieve 32 (or less).
Pro of Nottingham - more history to the university. Nottingham University is well known in Law circles.
Pro of Exeter - if this counts as a pro to you - more students who went to private school. But, since much of the Exeter campus looks quite modern, it might not 'feel' particularly private school.

The fact that Exeter attracts more private school kids is a result of the uni wanting to attract them to boost the image of the uni. Most Russell Group universities have gone above and beyond to reduce the intake from private schools. Also the fact that a school is private isn't an indication necessarily of good education, as plenty of mediocre private schools exist, as well as the elite ones.
On a more important point, Exeter has a nicer city, with less crime, but it is quite out of the way. Nottingham has the better Law school, but the gap isn't very big. Nottingham as a city isn't that nice, but all you need is on campus, and the location is more central, with great links to most other major cities by train.

I have gotten offers from both Nottigham and exeter for the LLB. Nottigham has offered me 32 and Exeter has offered me 34-36 IB points and I am not sure which one to ensure? Someone pls give your pros and cons and any experience visiting the city! Thank you

Can anyone tell me about the night/ social life in both these places from your experience?

Topuniversities.com regards Nottingham University as the 95th best place in the world for Law and Exeter University as somewhere between the 201-250th best place for Law.
If Nottingham University didn't have an attractive campus or some attractive accommodation, I wouldn't let rankings alone sway me, but it is generally regarded as attractive.
Graduate prospects are deemed only slightly higher at Exeter for Law students in general so, considering the 30% Exeter v 18% Nottingham private school difference, Nottingham is almost certainly technically batting above Exeter in terms of added prestige compared to where each student on average originally came from. The percentage of Law graduates currently doing something related to what they wanted to do is identical at each place.
Lastly, edurank regards Nottingham University as the 10th best in the UK (12th best in Europe, 62nd in the world) for Law and it regards Exeter as 23rd in the UK (37th best in Europe, 136th in the world) for Law.

You don't just state 30% and 18% randomly for private school intake. The actual numbers of kids from this section of society is about the same in both universities. The difference between the two universities is that Nottingham takes on more state school students, and most of those will be from good state schools.
Remember that many top universities, including Oxbridge, Bristol and Edinburgh, have gone out of their way to reduce their private school intake, resulting in a more even intake among the Russell Group.
Private schools coach their students to succeed. They aren't all that clever in general.

As Exeter University has about 20,000 undergraduates and Nottingham University has about 26,000, there'll be about 6000 private school students at Exeter University and about 4680 private school students at Nottingham University. Although not that dissimilar as numbers, Exeter is also a smaller pool of people so it's a notable difference. Although, specific to the Law department, I couldn't find figures.
As you say, because of some excellent state schools, the general class level might not be dissimilar, not that that matters so much any more when top universities such as Oxbridge are actively trying to increase state school intake (and some have reached the stage where they realise that it isn't necessarily fair to swing too far that way).
At the end of the day, we all make only so many close/true friends at university and, with so many people, it's sometimes as easy to find likeminded/similar histories, or differently minded/different histories, people as people want to make it. I think environment partly determines outlook and I think that Nottingham probably makes it easiest to live in for most personality types, because it's a big city.

Thank you both for such insightful responses! Do you think that Nottigham would give me a better edge at magic circle law firms?

I have found no more recent data on this than a chamberstudent report from 2019 which said that 5% at London City firms (not necessarily just Magic Circle) came from Exeter University, 4.5% from Nottingham University.
Of course, as Exeter is more south, more Exeter graduates might have applied to work in London firms. But, outside of the capital, 4.8% were Exeter graduates, 5.2% Nottingham graduates. I can't find stats on the number of law students at each university but Exeter University has about 20,000 undergrads, Nottingham University about 26,000.
It appears that, before 2016, Exeter University was not so much on the radar for either students or firms for Law, compared to Nottingham.

I don't think it matters which one you attend out of these, as long as you have AAB or better at A level (or the IB equivalent), and minimum 2.1 degree. After that come the interviews and assessment centres, and possibly some online tests beforehand. Work experience is also highly valued, as is high level connections in the profession.

Your assertion "as is high level connections in the profession" is incorrect, as well as ungrammatical.
More generally, university rankings, and all those old and irrelevant statistics which fascinate some posters here have ZERO relevance to the individual career prospects of anyone now considering a legal career. University-blind recruitment is now widespread, and no law firm which wishes to make profits is so foolish as to recruit simply on the name of a candidate's university (and still less on the basis of "connections").

Of course it matters if you have high level connections in any given profession. For example, why do you think families where at least one parent is a Vet or a Doctor also tend to have children who also get into the profession?
As for grammatical errors, l type so fast on my phone that it is inevitable that a few errors will creep in here and there. What is more, J.R.R. Tolkien made a few errors of his own in the LOTR novel, and they remain there to this day.

It is quite commonplace for children to follow a career similar to one or both parents, but that does not mean that "high level connections in a profession" are, as you suggested above "valued". If you assert that a candidate who has "connections" is likely to be more favourably treated by recruiters because of such "connections" than another candidate, that is for you to prove. Do you imagine that at interviews candidates are asked who they know in the profession? Have I and my colleagues who recruit new entrants to the legal profession been missing something by failing to check on the "connections " of the candidates we assess? Do you have any relevant experience on which you base your assertion?

Connections often mean internship and mini pupillage opportunities, or some shadowing work experience. Only an ignorant person would think otherwise. It is what David Cameron relied upon to get his breaks into politics as a graduate and beyond.