Let's hope we see each other again soon!
'Speriamo' — spe-RIA-mo. Stress on the second syllable. 'Rivederci' — ri-ve-DER-ci, stress on the third syllable.
Use when there's some uncertainty about when you'll meet again — you hope it will be soon but you can't promise a specific date. Warm but realistic.
'Speriamo' (let's hope — we hope) uses the subjunctive mood of 'sperare'. 'Di + infinitive' follows: 'speriamo di rivederci' (we hope to see each other again). The 'presto' (soon) adds optimism. This farewell expresses genuine desire for reunion.
Speriamo che ci si riveda presto.
Let's hope we'll see each other again soon.
With subjunctive clause — 'che + si + riveda' (the impersonal reflexive)
Spero di rivederti al più presto.
I hope to see you again as soon as possible.
More personal — 'ti' instead of 'ci' addresses the person directly
Non perdere le nostre tracce!
Don't lose track of us!
Idiomatic — 'perdere le tracce' (to lose the tracks of) = to lose touch. Playful.
'Sai dov'è casa' (you know where home is) is a powerful Italian hospitality phrase — it means my home is always open to you. Said sincerely, it's an open invitation. Italian hospitality ('ospitalità') is considered a virtue and a duty — the guest is sacred.