All this talk of which GPS assumes you need one at all.
As already mentioned, you can determine your coordinates from, e.g., Google Maps beforehand - within a few hundred metres is quite accurate enough.
You can get time from your phone - I've used a cordless phone from the yard dialling 1194, but that also works from a mobile (at least on Telstra and Optus but I expect all of them).
Mobile network time, in my experience, is out by up to a minute*, so I wouldn't use that. But if you have a smartphone, you can go to
http://time.is/ to see accurate time - it corrects for network delay and I've compared it to NTP servers and found it to never be out by more than a second ... or maybe it was the NTP servers I was using that were out, either way it's in close agreement with authoritative time sources.
* The interaction between phone handset and mobile time update is not easy to configure - my phone has only on and off settings, and I can't see network time directly - I suspect the mobile handset updates infrequently and drifts a lot.