Meditating with the eyes open allows more connection to the sensory experience, while meditating with the eyes closed provides more insulation from distraction. There are advantages and disadvantages either way. With less distraction, it's easier to stabilize the mind; this might be very helpful for some people. On the other hand, with less sensory input, it's easier to get lost in your own little world, lost in wandering thoughts, lost in experiences of bliss that might arise from strong states of concentration. In addition with long-term practice it's somewhat easier to develop a sense of separation from the world, which is different from "non attachment" and can lead to people acting like they're better than everyone else, etc.
On the other hand, with eyes open and more sensory input, it may be overwhelming and difficult to stabilize the mind at all. Only a few people are probably capable of doing any kind of meditation while, say, staring at a busy street scene in Manhattan (but some are!) But on the other hand, the meditation practice that does develop will be more ensured to maintain a connection with the senses and the outside world. It is more likely to develop an equanimity and mental stability that is tolerant of the vicissitudes of the outside world, rather than an equanimity that compels one to "run away" to the forest, the mountains, the monasteries.
There is somewhat of a tendency that traditions emphasizing individual liberation from suffering teach meditation with the eyes closed; while traditions emphasizing first the development of compassion for others teach meditation with the eyes open. (Because of the differences mentioned above.) Nevertheless, in either case, there is some wiggle room for whatever works best for the individual at her/his current stage of development.
If you practice with a qualified teacher, someone who is good at deeply perceiving you rather than merely spouting lists of instructions, then they will be able to give you good advice. Otherwise, feel free to experiment, keeping the opposing considerations in mind, and find a good balance for yourself.