I live in Rumson. Fair Haven and Rumson share the same high school. I coach baseball and soccer, and I envy the programs they have in Fair Haven. I also like their downtown (Rumson does not really have one). Closer proximity to Red Bank is a plus too. Don't really see any negatives or downsides. Given the choice to do it again, we would have picked Fair Haven over Rumson. You will love the annual Fair Haven Fireman's fair which is the last week before Labor Day every summer.
Are you going to take the Ferry from Highlands or Atlantic Highlands?
A couple of local parks/sites that are worth checking out are:
1. Hartshorne Woods--go to the entrance at the top of Portland Road-- great views, and an old military battery on the top of the hill; Outstanding hiking and mountain biking trails.
2. Twin Lights in Highlands- you can go to the top of the lighthouse.
3. Mt Mitchill park in Atlantic Highlands/Highlands--spectacular views of Sandy Hook and NYC
4. Sandy Hook. Great paved trail for running, biking etc, and lots of interesting military buildings and artifacts.
5. Huber Woods in Middletown- nice wooded trails and a learning center and a cool reptile house.
Good luck with the move. If you need a local attorney, Brooks von Arx is a good real estate attorney.