Is there a way to avoid entering my password in new SSH windows?

You may get around repeatedly entering your password and multifactor information by setting up an entry in ~/.ssh/config on the local workstation. Add something like the following

Host caltechhpc

Hostname login.hpc.caltech.edu

User jflilley

ControlMaster auto

ControlPath ~/.ssh/control:%h:%p:%r

Save the file and try connecting to the cluster with 'ssh caltechhpc'. At this point, you should be able to login once with password and multifactor authentication. All subsequent connections should re-use this information without additional steps.