If I get Great Library and slingshot Philosophy (and, I'd hope, have a good production and food capital with decent gold), I'd consider building NC immediately after GL. If my city sites will be there 10 turns later, it's not too much of a loss to get NC out of the way immediately. Just don't get complacent and forget to settle cities at all. You could go for Philosophy without GL and 1-city too, but that means being way too slow in the race.
Otherwise, there's nothing wrong with waiting for 4 cities to work on NC, and waiting until after Civil Service to research Philosophy->Theology->Education. That gives ample time to set up production and food, and comes with money and military stuff. So long as NC is complete before Education and Education is reached at a reasonable time, exactly when is not that big a difference. Science without gold and hammers to put it to use is often overrated.
Another possibility - build the 4th settler, then start NC, wait for NC to finish before founding city 4. Depending on city site, this might only mean a few turns delay in settling the city, as travel will take time.
In a tradition game, I like to be sure my 2nd city is able to build settlers, so my cap is freed to build more useful stuff. The less time my cap spends building settlers, the better it is for that cap to prepare good stuff.
There are some pretty good wonders to grab that compete with early NC.
Stuff like map conditions play a role too. Really depends on how many good production sites I can get, and if I can rush a library somewhere. 2 city NC is generally the worst, and 3 city NC isn't too bad if Philosophy is a higher priority for you/CS is a lower priority (say you have no fresh water in the capital or any of your cities - and that's a pretty horrible situation for a Tradition start, but you'd work with what you're given).
If playing Liberty then NC doesn't necessarily need to be in the cap, but it shouldn't be put off for too long in any start... unless doing some despotic conquest thing, in which case NC is superflous. Even for Liberty strategies, getting NC early shouldn't be dismissed... just because Liberty wants lots of cities doesn't mean they have no vertical expansion, and NC at the right time can be really useful for supporting long-term expansion. It's just less valuable than a tradition NC capital.
If I do play Liberty, I'd like to have a reasonable shot at GL, and use the free settler to offset the hammers sunk into it. Seeing Tradition players miss GL makes me a happy camper.