Alterac valley in PvE.
If you are in AV, you are doing PvP whether you like it or not, unless you leave the battleground.
But that said, there are a lot of quests in AV that gives it a more PvE feel than the other battlegrounds.
If you are interested in using AV as an introduction to PvP battlegrounds, I have written a guide based on the assumption that this is your first PvP experience.
Gnomer and Out!