Myslím, že je lepší být s rodinou než s telefonem.

In Czech, subject pronouns (like já, ty, on) are usually omitted because the verb ending already shows who the subject is.

• myslím = I think (the -ím ending tells you it is já)
• myslíš = you think (singular)
• myslí = he/she/they think or you think (formal)

You can say Já myslím, but it is more emphatic, like I think (as opposed to someone else). In neutral speech, Myslím, že… is the most natural.

Both myslím and myslím si are correct here, and both mean I think. The difference is subtle:

• myslím – neutral, very common.
• myslím si – can sound a bit more personal/subjective, like I believe / I’m of the opinion.

In everyday speech, you will hear both:

• Myslím, že je to dobrý nápad.
• Myslím si, že je to dobrý nápad.

In your sentence, Myslím, že je lepší… and Myslím si, že je lepší… are both fine.

Czech almost always puts a comma before že when it introduces a subordinate clause (a dependent clause).

• Myslím, že je lepší…
  
  • Myslím = main clause
  • že je lepší být s rodinou než s telefonem = subordinate clause (what you think)

So the comma is required by Czech punctuation rules.

že corresponds to English that (in I think that…).

• Myslím, že je lepší… = I think that it is better…

In English, that can often be dropped: I think it’s better…
In Czech, že CANNOT be dropped in this kind of sentence.

You cannot say:

• ✗ Myslím je lepší být s rodinou…

You must use:

• ✓ Myslím, že je lepší být s rodinou…

The structure is:

• je lepší být… = it is better to be…

je is the verb být (to be), 3rd person singular present (is).
Czech usually needs this je in such impersonal evaluations:

• Je dobré se učit. – It is good to study.
• Je těžké to vysvětlit. – It is hard to explain it.
• Je lepší být s rodinou. – It is better to be with (the) family.

Without je, the sentence is ungrammatical:

• ✗ Myslím, že lepší být s rodinou… – wrong
• ✓ Myslím, že je lepší být s rodinou… – correct

The preposition s (with) requires the instrumental case.

• rodina (family), nominative → s rodinou (with family)
• telefon (phone), nominative → s telefonem (with the phone)

So the pattern is:

• s + instrumental
  
  • s kamarádem – with a (male) friend
  • s mámou – with (my) mum
  • s rodinou – with (my/the) family
  • s telefonem – with the phone

Using s rodina or s telefon would be wrong, because those are nominative forms, not instrumental.

They belong to different noun declension types.

• rodina – feminine noun (ending in -a)

  • Instrumental singular: usually -ou
  • rodina → s rodinou

• telefon – masculine inanimate noun (ending in a consonant)

  • Instrumental singular: usually -em
  • telefon → s telefonem

So both are just regular instrumental endings for their noun types.

• s
  • instrumental = with someone/something (in someone’s company, physically together)
    
    • být s rodinou – to be with family
    • být s telefonem – (literally) to be with the phone, spending time with it

Other prepositions mean something else:

• u telefonu – at/by the phone (e.g. answering a call)
• u rodiny – at the family’s place (at their house), not with them in general

Your sentence contrasts the company you keep:

• být s rodinou vs. být s telefonem

Here, lepší does not directly agree with rodinou or telefonem. The structure is:

• je lepší být s rodinou než s telefonem
  
  • literally: it is better to be with family than with the phone

lepší is in the default (masculine/neuter) form because it goes with an implied to (it):

• (To) je lepší. – It is better.

The comparison is between two infinitive phrases:

• být s rodinou
• (být) s telefonem

You don’t change lepší for those; you keep lepší the same.

Both versions are grammatically correct:

• Myslím, že je lepší být s rodinou než s telefonem.
• Myslím, že je lepší být s rodinou než být s telefonem.

In Czech, if the verb is the same in both parts of a comparison, you can omit it in the second part:

• Raději budu doma než v práci.
  (than [I’ll be] at work)

Omitting být after než here makes the sentence a bit shorter and more natural in speech, but including it is also fine.

Yes, that sentence is completely correct and natural:

• Myslím, že být s rodinou je lepší než být s telefonem.

Here you have:

• být s rodinou as the subject of the clause
• je lepší as the predicate

Both word orders are fine, just slightly different in focus:

1. Myslím, že je lepší být s rodinou než s telefonem.
   – It is better to be with family than with the phone.

2. Myslím, že být s rodinou je lepší než být s telefonem.
   – Being with family is better than being with the phone.

Same meaning in practice; both are good to use.