Some universities have publicly accessible servers:
pool.ntp.org has NTP server pools for many countries.
First: be nice! You shouldn't synchronise to a stratum 1 server for your small network -- if everyone did that then the server would need too much bandwidth. For example. NetGear? hard-coded a public NTP server into some of their consumer products, which eventually ended up using hundreds of Mbits/second of the university's bandwidth, even after they were forced to shut down the server.
The difference in accuracy between syncing to a stratum 1 server and a lower stratum server is negligible.
There are three stratum 1 NTP servers provided by .nz Registry Services (NZRS) for network operators based within New Zealand.
All three are Symmetricom S300 NTP servers, each connected to a differential GPS antenna on the roof and each with a rubidium oscillator to provide a stable clock in the event of an issue with the GPS signal. more
They are FreeBSD-based servers that are directly connected to their master HP5071A caesium clock. more
The US National Institute of Standards and Technology (NIST) operates several publicly accessible stratum 1 time servers on the Pacific coast of the US. These servers are referenced to UTC(NIST) using the NIST Automated Computer Time Service (ACTS), a MoDem-based service established in 1988.
The US Naval Observatory (USNO) operates several stratum 1 time servers from its Alternate Master Clock Facility (AMCF) at Schriever Air Force Base, near Colorado Springs, on the same site as the GPS Master Control Station. These servers are referenced to UTC(USNO).
Hurricane electric operates several stratum 1 servers with good connectivity on the Pacific coast of the US.
The Australian National Measurement Institute (NMI) maintains the Australian time standard, UTC(AUS) using caesium and hydrogen maser standards. NMI maintains a number of NTP servers which are referenced to UTC(AUS). To use these servers, you need to register via Email.