I suspect you'll be going to Oxford.
I am not sure if you have been before but it is a beautiful place and I am sure you will fall in love with it. However, it is spread over a wide area and some of the colleges are away from the centre, so I would recommend you prioritise what you want to achieve before you go.
As you want to read Classics you must go to to their presentation and perhaps a taster lecture if there is one (maybe contact them in advance to find out and get the times).
FWIW when I last went to an open day I thought about the questions I wanted to ask
before I went and wrote them down. These ranged from the domestic, to course details and questions about the amount/type of work I would be doing. I came away with all my answers and had a better understanding of college life, the course and of what college to apply for.
I would also suggest that you have a look through some of the college websites before you go, this will give you a major head start (eg
https://www.sjc.ox.ac.uk/).
I know that a few people here have suggested that they don't really mind where they'll end up, and may even make an 'open application', which is where you make no preference and are allocated a college. However, there are big differences in
size,
wealth (freebies and support),
location,
politics (eg The People's Republic of Wadham),
people, facilities,
where you will live each year (some send you out to shared houses some way away in certain years - others house you in or near college throughout your time there) etc.
Because of the sometimes huge differences I would say time spent ahead of your trip looking at college websites will be a great start and, if you do like the sound of, say, St John's (central, brilliant facilities and RICH) then you can try to go to the college and speak to staff and students there - they will all be friendly and you will learn so much.
It'll be a great day, but you will get so much more out of it if you plan in advance.
Finally, if you've never been, I would recommend you spend 10 or 15 mins having a look at a (Google) map of the colleges, so you can get a feel for where each of them are in relation to important facilities and also get a sense of scale - you'll feel more familiar with the place when you get there!
Best of luck and maybe I'll see you at the Classics presentation (you can recognise me by my avatar).
G D'G