I have an offer to do a PhD in Computer Science from a fairly new university. The research topic is good but I can't really decide what are positives and negatives of it.
Well, the first thing to think about is what sort of new university this is. If it's UC Merced, then you might reasonably guess that it will eventually be as well known as the typical UC campus, and of course that's not the only new university intended to be very prestigious and successful (e.g., IIT Indore). On the other hand, most new universities just don't come with this sort of commitment and backing. If you don't have a powerful reason to think the university will be unusually successful, then you should assume it's headed for a not particularly distinguished future. Furthermore, the initial years may involve growing pains that would not be present in a better established university, although these issues are not likely to be a big deal.
Now, this isn't a reason not to study there. Most universities are by necessity not particularly distinguished, but that won't stop you from getting a decent education. However, the key thing is to avoid getting caught up in a feeling of "Wow, a new university! What a great opportunity to start from scratch and do everything right! I'm sure we'll avoid all the mistakes that have held other schools back." Helping to start something new really is exciting, and it can be a wonderful experience. However, all new projects start with high hopes, while history shows that most never fully meet these expectations.
So the real question is how much these high hopes matter to you. If the new university turned out to be a solid, respectable school but not highly ranked or especially successful, would you regret having gone there? If not, then there's no problem. (I'm assuming it's definitely a respectable option, and not for example an online diploma mill.) If so, then you should think carefully and investigate whether their plans really look feasible. For example, by looking at what sort of faculty have they managed to recruit so far.