The tenses in all your examples are perfectly fine.
I believe that in the last example you could have switched to present perfect if you wished so it would look something like:
Mike asked why you didn't come to the party with me, but I explained to him that you have been working hard for the past two weeks, and now you're free all you want to do is get some rest.
(I hope I got my present perfect right, I'm not too hot at grammar terms.)
Note that you probably want to say 'but I told him it was because...' or 'but I told him that it was because...'. In the final example you wouldn't normally have 'me' twice in the first part, you'd say 'Mike asked why' or 'Mike asked me why you didn't come to the party, but...'. In casual speech you'd probably get away with it, though.
The sentence, "I would leave tomorrow", is grammatical, but is lacking some sense (subjunctive mood)
The Subjunctive Mood
A verb is in the subjunctive mood when it expresses a condition which is doubtful or not factual. It is most often found in a clause beginning with the word if. It is also found in clauses following a verb that expresses a doubt, a wish, regret, request, demand, or proposal.
Source: http://englishplus.com/grammar/00000031.htm
"If I would leave tomorrow..." (correct)
ALSO:
(1) I was going to leave tommorow. <- WRONG (tomorrow indicates a future time reference, you cannot use it considering the context you provided)
"I am going to leave tomorrow." (correct, the day before leaving)
"I left [yesterday]." (arrival)
(2) I was leaving tomorrow. <- WRONG (same as above)
"I will be leaving tomorrow." (correct, the day before leaving)
"I left [yesterday]." (arrival)
I will not discuss the use of past progressive here, but I'll provide a link http://www.englishpage.com/verbpage/pastcontinuous.html
*I left tomorrow. <- WRONG (same reason)
You cannot say, "I ate tomorrow" in the same way that you cannot say "I will eat yesterday".
per definition:
tomorrow
[tuh-mawr-oh, -mor-oh]
noun
1.
the day following today:
Tomorrow is supposed to be sunny.
2.
a future period or time:
the stars of tomorrow.
Since 'tomorrow' is a future time reference, it is wrong to use it in the above quoted sentences. The point here is you cannot simply use a future time reference in a sentence referring to a past action. Also, it is ungrammatical to say "I would leave tomorrow" (in the context the OP provided). 'Will' is a modal used to indicate future tense, hence the main verb's tense should be changed. As above explained, you may use it if you are indicating a subjunctive mood.
Remember that leave/leaves (present); left (PAST); and will leave(future).
Best Answer
The OP believes that It would be nice to see you before I left expresses a wish and not a real situation, and this is why the past tense is better in the subordinate clause.
It is certainly true that wishes that a present situation were different are commonly expressed in the past tense:
It is also true that the past tense is typically used in the subordinate clauses of similar (so-called) conditional 2 sentences to express an unreal (counterfactual) situation:
The past tense is also used in conditional 2 sentences to convey the speaker's belief in the remoteness of the possibility of something happening:
Further, the past tense is common (but far from mandatory) in the subordinate clauses of reported statements:
But none of the above contexts fits the OP's example. The It would be nice to see you clause in this context does not mandate the past tense of the verb in the subordinate clause.
The leaving is prearranged, hence the present tense is used. There is nothing unreal or counterfactual or reported about the leaving. The present tense is the usual tense for scheduled events: cf. My plane leaves at 8.45 tomorrow evening. So, my clear preference in this context is for:
Two further points. Firstly, the main clause can be expanded to: It would be nice if I could see you .. , in which case the past tense (could) is used to express a wish, remote possibility or counterfactual. But this still has no influence of the tense in the before I leave clause.
Secondly, the past tense is often used to express deference or politeness. For example:
So, It would be nice to see you before I left is conceivable in the context of, for example, a student requesting an appointment with a professor.
Addendum
The list below shows the Google results for various "It would be [ nice / good / great ] to [verb] ... before I ... " constructions. They show that the present tense is much more usual in the before clauses of such constructions.