Unico vs. solo
While both unico and solo can translate to only in English, they are not interchangeable. Unico emphasizes uniqueness or being the one and only, while solo typically refers to being alone or is used as an adverb meaning just or only to limit a quantity or action.
Unico
A2Unico is an adjective that means unique, one-of-a-kind, or the only one. It highlights the singularity of a person or thing, implying there are no others like it. As an adjective, it must agree in gender and number with the noun it describes (unico, unica, unici, uniche).
Questo è l'unico modo per risolvere il problema.
(This is the only way to solve the problem.)
La vista da questa montagna è un'esperienza unica.
(The view from this mountain is a unique experience.)
Marco è il mio unico amico in questa città.
(Marco is my only friend in this city.)
Le uniche persone invitate erano i parenti stretti.
(The only people invited were close relatives.)
È un pezzo unico, fatto a mano dall'artista.
(It is a one-of-a-kind piece, handmade by the artist.)
La sua unica figlia vive all'estero.
(Her only daughter lives abroad.)
Solo
A1Solo has two main functions. As an adjective, it means alone, lonely, or by oneself, and it agrees in gender and number (solo, sola, soli, sole). As an adverb, it is invariable and means only or just, typically limiting a verb, quantity, or another part of speech.
Stasera preferisco restare a casa da solo.
(Tonight I prefer to stay at home alone.)
Voglio solo un po' di tranquillità.
(I only want a bit of peace and quiet.)
Maria si sente spesso sola la domenica.
(Maria often feels lonely on Sundays.)
Mancano solo cinque minuti all'inizio del film.
(There are only five minutes left until the movie starts.)
Siamo rimasti soli a pulire tutto.
(We were left alone to clean everything.)
Ha detto che era solo una scusa.
(He said it was just an excuse.)
I bambini non dovrebbero mai essere lasciati soli.
(Children should never be left alone.)
Summary
In essence, use unico to stress uniqueness or the fact that something is the one and only of its kind. Use solo when you mean alone or lonely (as an adjective), or only/just to express a limitation (as an adverb). A simple test: 'L'unico uomo' means The only man (implying no other men exist in that context), whereas Un uomo solo means A man who is alone.