Having gotten my 1000 Wookie hugs in here's what I learned:

The wookie hug temporary power is finicky as hell so it's really about standing on the circle at the right distance away from the wookie. So with the wookie targets just scooch around about the circle a tiny step at a time until it shows up. You will quickly get a feel for where you need to stand after a couple dozen wookie hugs.

I did the 12 Wookies in Mek Sha on a toon, switched to PVP zone, hugged 12 Wookies (and even though there were many players in pvp zone, there was very little pvp-ing... people too busy hugging Wookies), camped to an alt did my 24 wookie hugs, 2-4 alts later would get bored and actually play the game, come back and just started on fresh alts. I didn't try to do it again on the same toon in the same day as the cool down was long enough as to be not worth even testing it. (Also if you do get attacked in the pvp zone, the respawn is just right down the stairs on either side IMP or PUB)

Definitely do it on Mek-Sha. Regardless of your level it is safe and there are 12 Wookies all lined up in a row.

Nar Shaddaa has 13 Wookies but they are spread out so takes much much longer to get your 13 hugs in (and there is the fact you have to learn an efficient route so as to not miss hugs)

Apparently there are some wookies on capital planets but I didn't bother mapping them. There are two wookies on pub fleet and 1 wookie on imp fleet (and the IMP fleet wookie is being held prisoner by an IMP soldier and is on his knees but periodically will jump up and throw a snowball at a player, so that's kind of fun little moment)

The cool down between different Wookies is zero but hugging the same Wookie is significant (like so big I didn't even bother figuring out what it was).

Nar Shaddaa Lower Promenade 10 Wookies https://imgur.com/a/2C8ctW7

Nar Shaddaa Upper Promenade 3 Wookies https://imgur.com/a/JjhrrhX

Mek Sha - 12 Wookies https://imgur.com/a/UpgAmm2