I completely agree with what
@jta227 and
@Jessica Booker said. I only have two things to add. Firstly, I think it would be beneficial to do some extra research on the firm, which will allow you to naturally discover questions you might have an interest in asking. I would specifically target my research around the firm's unique selling points which I would consider using in a VS/TC application. This is both because I would have an actual interest in learning more about those aspects of the firm (so, I could make a good impression without looking like I am trying too hard) and because getting more information on those points is what would enable me to write a better VS/TC application. To give an example, when I recently attended an insight event at
Davis Polk, someone asked about the firm's plans for its London corporate practice, as the firm had recently invested in a number of top lateral hires. This shows off the attendee's research but is also a genuine query that has a bearing on their decision making if they have an interest in doing a certain type of corporate work. Furthermore, the response someone from someone at the the firm can often be more nuanced and insightful view than can be found in the legal press, and will thus enable the attendee to write a more impressive application.
Secondly, if you have the opportunity, I think it is a good idea to go and say hi to the graduate recruitment team. As the other members said, definitely avoid going looking like you just want to impress. Instead, if your attitude and intention is just to try to get to know some people at the firm and learn about their experiences, I cannot see how this could negatively impact you. Quite the opposite - if the graduate recruitment team sees you as nice and sociable, the kind of person they might enjoy chatting with over a coffee, they might remember you when they are reading your application or reviewing a VI. This will not have a decisive influence on the ultimate outcome, but in a game of such small margins everything helps.