You do not need to use a past tense verb in the 'that' clause if the main verb is in the past tense.
If something is still true now, it is better to use present simple after 'that'...
'Yesterday, he said that it's a nice place to visit' - said that + present tense
It is also possible to use past tense after 'that' in this situation with the same meaning - 'Yesterday, he said that it was a nice place to visit' - but as you can imagine, it could be quite confusing.
The other main tense that we use after 'past tense + that...' is something called future from the past:
Future from the past usually talks about things in the future from a past perspective, that have usually already happened at the time of speaking
'He said that he would help us' - said that + 'future from the past'
He said in the past that he would help us in the future. The helping has already happened by the time of speaking.
'I knew that it was going to rain' - I knew in the past that it was going to rain in the future, and now it is raining.
'I didn't think we would lose the game' - In the past I didn't think we would lose, but now we have lost.
Here is some more information about talking about the future from the past: http://dictionary.cambridge.org/grammar/british-grammar/future-in-the-past
If something STILL HASN'T HAPPENED at the time of speaking, we would use this structure:
'He HAS said that he will help us' - HAS said that + future
He has said in the past that he will help us, the helping has not happened yet