Context: Yokoi Rumi 横井るみ introduces the series title character.
watashino tonari no seki no Seki-kun wa juuygou-chuu itsumonanika shite asonde-iru 私の隣の席の関くんは従業中いつも何かして遊んでいる Seki-kun, [who sits next to me], is always playing doing something during class.
watashi no tonari - next of me (neighboring me).
watashi no tonari no seki - the seat that is next of me, the neighbor seat.