I've created some 2D animations in After Effects, which are supposed to take place in the 60s & 70s.
Is there a way I can filter these in Premiere (or AE or anywhere else) to give the user the impression that the scenes could possibly be taking place in the 60s or 70s? In another world or time period?
Without simply going to black-and-white? Because black-and-white doesn't make me think of 60s & 70s.
It all depends on the particular look you want. A lot of stuff in the 60's and 70's was shot on film stock, so you might want to go with a film stock setting (Technicolor for example) if that's what you want, plus a lot of footage was shot with lower resolution video cameras (whites a bit blown out, poor color saturation, scan lines), so that's a different look. The film stuff might have things going on such as gate weave, dirt and hairs passing through the gate, and a slower frame rate, which would give a "softer" look, while the video stuff would have different color footprints.
You'd get the most control using Red Giant's Magic Bullet Looks, but it's expensive. Here's some free film looks: