It's a strange situation re: Albion rivalries. I'm not sure if you know the rough georaphy of Brum/Black Country.
The Hawthorns is right on the border of Brum (literally yards outside the city boundary) and just approx 3 miles from Villa Park, 6miles from Blues but 12 miles from Molineux, so Villa SHOULD be our rivals, but then you have the geography of support, most of which for Albion & Wolves is based in the Black Country.. Smethwick, West Brom, Dudley, Tipton, Cradley, Wednesbury etc so for the majority Wolves is THE Derby.
Me and my mates live in Smethwick, close to (but NOT in) Birmingham, so growing up in the 70s it was always VIlla as our main rivals and for me still is.
It's a bit confusing.. probably best to hate all of them to be safe.