I'd like to treat you to dinner next week, so please accept my invitation.
Literal
Next-week you [to-に] dinner [object-を] treat-want [because-ので], somehow this invitation [object-を] receive-accept please.
おごる ('to treat [someone] to / stand a meal') is casual-to-neutral. どうか ('please / somehow') is a pleading/imploring softener more emotional than ただ ('just'). 受け入れる is a compound verb: 受ける ('receive') + 入れる ('put in') = 'to accept / take in.' ので is the objective-causal 'because.'