I am writing a time travel story. Where should I make my characters go?

Or just have the characters be genre-savvy enough to explain those things themselves. If someone was really doing time travel stuff, they'd probably talk about these things with their time travel buds.

 

"I'm going to go back and talk with my grandfather. He was such a great man, my dad says, and I never got to talk to him. He died while I was still a baby," I say.
"What are you going to talk about?" Christa asks.
"I haven't put any thought to it. Maybe I'll tell him who I am and tell him how I got here."
"I don't recommend that."
"Why?"
"Because if you let him in on too much, you might change too much. It could end with a temporal paradox." She's got a point. I mean, would me telling him that I'm his grandson make him not make my father and in turn keep me from being born?
"You're right." I'm not risking it.

I mean yeah, but that right there is very corny (then again I just kind of scribbled it down). It'd have to be very well done.

 

@Ulramar , @MLM :

Guys, you misunderstood me The writer should be aware of these paradoxes not the reader. You don't even need to explain the paradox but need to understand it to be able to write a logically intact story.
Readers have a good understanding on how the real world works and they also have an idea of time travel (especially sci-fi fans). If you write a time-travel story in which the MC goes back in time and kills his grandfather before he meets his grandmother then you can't just make him return "back to the future" and continue his life as before. It is no wonder that the reader will expect major changes to happen in the new alternative future where one of his parents was not born so the MC never existed. He will definitely have problems with the police (he has a "fake" ID) and even his best friends will not know him. This is logical for most of the readers and if it doesn't happen you need to explain why (especially if his grandfather is still alive).

That's what I wanted to express, sorry if I was not clear at first. I listed the terms only to help writers google for useful time travel related info.

 

Oh, this exact topic reminds me a little bit of the old game Timesplitters (2000). Time travel is very interesting to play with and I believe I'm on the same field as you are. The only thing is my motives for time travel are for assassinations and completely changing history. As one poster said, time travel is very theoretical and it's amazing what you can do.

What I would do with time travel:

Prevent a world disaster from happening (One character in a short fiction piece I wrote attempted to prevent 9/11, but died while doing it.)
Cause your own world disaster! (I had a character attempt an assassination on the Pope and blamed it on the "godless-Communist" Russians.)
Have your character invest in something that would be the "next big thing," such as the Internet, Google, and other things related to popular companies of today.
Have your character regret not asking that girl out, then gain the time travel ability to actually do what his heart desired.

Oh you can do so much. Have fun and play around with it. Try not to be "logical," for not everything based on a theory has to be.

 

Yes, the best thing about writing is that you can build your own world (and in this case time travel theory) and write an interesting story about it (or several ones). You can choose to go on the scientific way (eg. building a time machine), the fantasy way (magic) or use some supernatural power like a time-portal found in a cave, etc...
You can concentrate on the interactions of a modern human and the old culture, the effect he causes by changing history (that's what you are interested in as I understand) or simply make your hero "time-machine-wrecked" who just tries to get back to his own age and family (that's what I'm interested in).

Here I disagree. Not completely disagree but partly. Only your imagination limits the rules in a world you build for your story. These rules do not need to be logical, they can be completely crazy. The events inside the world however should follow these rules and be logical according to the world's logic.
If in one chapter the time machine is a spaceship which must go faster than light to make the time jump and a few chapters later someone uses his watch as a time machine then the reader will have unanswered questions at the end of the book.