In public places or with other people, I don't believe their is a time limit, but it should probably be advised to avoid anything that could cause scandal. That said, it also depends on age to a small degree. Younger people who live with their parents are more likely in need of closer supervision, but lets say someone marries late, their parents are deceased, non-Catholic parents, etc. they usually end up being the main person responsible for keeping away from improper situations.
Normally, engaged couples tend to spend more time together, as much of preparing for a wedding and life afterwards requires collaboration and organization before the event. From what I have seen, it is not uncommon for engaged couples to go to mass and confession together, as well as participate in devotions and other pious practices in order to prepare for marriage and set the tone for the life they are about to spend together. It was probably much different in other times when marriages were arranged but, like you said, this is the world we live in.
Personally, I think they should spend a lot of time together and make sure they really know each other, including faults. If they haven't become acquainted with the family, this is also a good time to observe how the potential spouse treats their parents, it might be eye opening.