I prefer the second form because the infinitive "to ask" or "that he ask" is more suitable than "he asks".
In both sentences, "marvelous" is mispelled and the main verb should preferably be in future or past tense, since the acts of recommending and writing about the recommendation cannot occur at the same time. (Unless you are multitasking on the internet, perhaps)
I recommend to him that he asks his guide for more information about the museum because it is marvellous.
I recommend to him to ask his guide for more information about the museum because it is marvellous.
This one has me stumped.
2 answers
DrWLS is correct. The tense of the main verb is off; the second verb should be subjunctive, not an infinitive, and subjunctives have no singular form.
Here's a better form of the sentence:
I recommended to him that he ask his guide for more information about the museum because it is marvelous.
Here's a better form of the sentence:
I recommended to him that he ask his guide for more information about the museum because it is marvelous.