Most year-round group rides leave from near the University, with the exception of the roundup (leaves from Ina and Oracle, so not that far from downtown either). I’d pick something near there, because that also gets you to the loop fast and has easy access to night life (downtown–Congress, Rialto, Fox, convention center, bars/restaurants, etc.). It also puts you close to the freeway if you want to get out of town (Mt. Graham, etc.).
I live on the east side right off the loop. Also good–great access to the mountain and some other fun foothills climbs, but a lot quieter at night (pros and cons) and it’s a trek to get to the bigger group rides early in the a.m., and a pain to get to the freeway. Can you tell I can’t wait to move back downtown?