Non-native speakers often struggle with constructing sentences with the word “suggest”. The following sentences are incorrect:
Please suggest me a good hotel.
She suggested me to visit that museum.
You could say instead:
Please suggest a good hotel to me.
She suggested (that) I visit that museum.
She suggested visiting that museum.
When it is used in a that-clause, you need to use the subjunctive, which is just the bare infinitive (no to):
We suggested (that) she go to the cinema on Friday nights
He suggested (that) he be more careful
Melanie has written a blog entry about this which could help further: