近所の怪しい活動に注意すべきです

Meaning: you should look out for any suspicious activity in the neighborhood

近所: neighborhood, neighbourhood, nearby, vicinity
の: to, of
怪しい: suspicious, strange, mysterious, dubious, doubtful, fishy, suspiciously
活動: activities, activity, active, efforts, action, operations, movement
に: in, to, on, at, into, upon
注意: attention, careful, caution, note, warning, heed, regard, advice, notice
す: s, the, be, su
べし: should, must, bei
です: is, be, are, am, that, away