Nodetool commands can be run locally but not on other nodes in the cluster.
If you can run nodetool commands locally but not on other nodes in the ring, you may have a common JMX connection problem that is resolved by adding an entry like the following in <install_location>/conf/cassandra-env.sh on each node:
JVM_OPTS = "$JVM_OPTS -Djava.rmi.server.hostname=<public name>"
If you still cannot run nodetool commands remotely after making this configuration change, do a full evaluation of your firewall and network security. The nodetool utility communicates through JMX on port 7199.