I have heard only good things about St. Nektarios: it's a beautiful area, friendly brotherhood, prayerful services, good chanting, excellent abbot, etc. However, you should know a few things beforehand:
1) The services are entirely in Greek. There's not a word of any other language.
2) You should most certainly call ahead, even if you only plan to visit for the day. (That goes for ALL monasteries. It's only courteous. Also, that way they can let you know if there is some special reason why you might want to adjust your plans...or they can adjust theirs to make sure someone is available to greet you.)
3) Women are allowed to visit, pray and seek confession at all monasteries in North America. They can even stay in special, separate guest quarters in many monasteries. Call ahead and inquire about availability.
Personally, I recommend staying wherever you decide to go for at least one night. Otherwise, it's unlikely you'll be able to attend a full day's worth of services. You'll be distracted from the car ride, rushed and won't really even glimpse "monasticism." You'll just be a (spiritually well intentioned) tourist. Of course, 24 or 34-plus hours won't really give you a full taste of monasticism, but at least you'll witness an entire day from your own perspective.
More information about visiting monasteries (attire, etiquette, etc.) is available on St. Anthony's Web site: http://www.stanthonysmonastery.org/VisitorInfo.htm
Scroll down. Much of what they have there (especially on the links on the left) is broadly applicable to many monasteries, especially St. Nektarios.