"Мне нравятся большие окна."

Translation: I like large windows.

[AnastasiaStyIes]

И я не могу лгать!

[deactivated user]

Why not "Мне нравится" here?

[YazykPineapple]

Because the subject of the sentence is большие окна which would mean that the plural form of нравиться is used. If we were only talking about one window then the singular form would be fine. Here's this sentence and a singularized version, with the important stuff in bold.

Plural: Мне нравятся большие окна.

Singular: Мне нравится большое окно.

[Cloutier_Patrick]

How would I say, "I like bigger windows"?

[AndreasWitnstein]

«Мне нравятся больши́е окна.» = “I like big windows.”
«Мне нравятся бо́льшие окна.» = “I like bigger windows.”

In Russian, the distinction between the positive versus comparative in the nominative plural for this adjective lies only in the stress.

In the nominative masculine singular, the ending is also different:

“big”      =‘большо́й’ m., ‘большо́е’ n., ‘больша́я’ f., ‘больши́е’ p.
“bigger”=‘бо́льший’ m., ‘бо́льшое’ n., ‘бо́льшая’ f., ‘бо́льшие’ p.

[Dotters]

My guess would be «Я люблю окна побольше.»

[AndreasWitnstein]

That would be “I like windows bigger.”.

‘побольше’=“bigger” is only used as an adverb.