 Re: preposition after the verb 'to invite'
Invite for + activity
Invite to + place/event
'Coffee' isn't a place or an event, so I'd agree and use 'for coffee'.
You will see 'dinner' used with both- it depends whether you think of it as an occaion, like a dinner party, os simply the act of eating.
Tea:
They've invited me to tea = a meal at about 5pm
They've invited me for tea = a cup of tea |