For NLTK 3.0, you want to use the ParentedTree subclass.
http://www.nltk.org/api/nltk.html#nltk.tree.ParentedTree
Using the sample tree you've given, create a ParentedTree and search for the node you want:
from nltk.tree import ParentedTree
ptree = ParentedTree.fromstring('(ROOT (S (NP (PRP It)) \
        (VP (VBZ is) (ADJP (RB so) (JJ nice))) (. .)))')
leaf_values = ptree.leaves()
if 'nice' in leaf_values:
    leaf_index = leaf_values.index('nice')
    tree_location = ptree.leaf_treeposition(leaf_index)
    print tree_location
    print ptree[tree_location]
You can iterate through the tree directly to get the child subtrees.  The parent() method is used to find the parent tree for the given subtree.
Here's an example using a deeper tree for child and parent:
from nltk.tree import ParentedTree
ptree = ParentedTree.fromstring('(ROOT (S (NP (JJ Congressional) \
    (NNS representatives)) (VP (VBP are) (VP (VBN motivated) \
    (PP (IN by) (NP (NP (ADJ shiny) (NNS money))))))) (. .))')
def traverse(t):
    try:
        t.label()
    except AttributeError:
        return
    else:
        if t.height() == 2:   #child nodes
            print t.parent()
            return
        for child in t:
            traverse(child)
traverse(ptree)