Starhowl san,
Konnichiwa.
テレビの横 & テレビの隣 are both “something next to the TV.”
According to the grammar textbook, when you use テレビの隣, the size or category of A should be similar to the TV.
When you use テレビの横, the size or category of A can be different from the TV.
However, many native Japanese speakers use them interchangeably for talking about small things.
Yuki 由紀
Team JapanesePod101.com