Come and visit us whenever you can!
'Trovarci' — tro-VAR-ci. Stress on the second syllable. 'Passare a trovare' = to pass by to find/visit.
Use as a warm, open-ended invitation extended at goodbye — you're welcoming the person back before they've even left. Very Italian in its forward-looking hospitality.
'Passare a trovare' (to pass by to visit) is the standard Italian expression for visiting — literally 'to pass by to find (someone)'. 'Quando puoi' (when you can) makes the invitation open — no pressure, but the door is always open.
Sai dov'è casa, passa quando vuoi.
You know where home is, come whenever you want.
Open invitation — the most generous form of Italian hospitality
La porta è sempre aperta per te.
The door is always open for you.
Idiomatic — 'la porta aperta' (open door) is a physical metaphor for constant welcome
Vieni a trovarci presto!
Come and visit us soon!
'Presto' (soon) adds urgency to the invitation — not just when convenient but soon
'La porta è sempre aperta' (the door is always open) is not just a figure of speech in Italian culture — Italian homes are traditionally open to family and close friends without prior arrangement. Dropping in ('passare a trovare') is normal in smaller Italian towns even today.