A linked list is a node with a value and a pointer to the next node. Finding the k-th item is Θ(n). Inserting after a node you already hold is Θ(1).

Goal

Build a short list of cities, walk it, and insert after the head.

Walk

class Node:
    def __init__(self, value, nxt=None):
        self.value = value
        self.next = nxt

def to_list(head):
    out = []
    steps = 0
    cur = head
    while cur:
        steps += 1
        out.append(cur.value)
        cur = cur.next
    return out, steps

head = Node("Nairobi", Node("Mombasa", Node("Kisumu")))
print(to_list(head))

Three nodes, three steps. No random access.

Insert after a node

class Node:
    def __init__(self, value, nxt=None):
        self.value = value
        self.next = nxt

def insert_after(node, value):
    node.next = Node(value, node.next)

head = Node("Nairobi", Node("Kisumu"))
insert_after(head, "Mombasa")
cur = head
while cur:
    print(cur.value)
    cur = cur.next

One pointer assignment. You did not shift Kisumu in an array — you retargeted next.

Find, then insert

class Node:
    def __init__(self, value, nxt=None):
        self.value = value
        self.next = nxt

def find(head, target):
    steps = 0
    cur = head
    while cur:
        steps += 1
        if cur.value == target:
            return cur, steps
        cur = cur.next
    return None, steps

head = Node("Nairobi", Node("Mombasa", Node("Kisumu")))
node, steps = find(head, "Mombasa")
print("steps to find", steps, "value", node.value)

The insert is cheap after the find. The find is linear.

Pitfall

There is no head[2]. If the recipe needs the middle often, use an array (Python list), not a linked list.