will replaying the story affect my character?

[Booshy]

So if you've done all the side missions, then finish the story mission, do the side missions open up again too as you go back through the main story missions? not that I really want to do those side missions again........

[WarMachine]

Also the big robot under Golden Gate Bridge returns when you reset so make sure you have the underpass fast travel already.

If you beat the main missions already, you'll have unlocked all hubs. The final mission is received at Underpass so its kinda impossible not to have.

[BrassRazoo]

So if you've done all the side missions, then finish the story mission, do the side missions open up again too as you go back through the main story missions? not that I really want to do those side missions again........

Not that I noticed no.
Just story only.
You complete a story mission then after a few minutes you are contacted and the next one opens up.

[mikegonzalez2k]

So if you've done all the side missions, then finish the story mission, do the side missions open up again too as you go back through the main story missions? not that I really want to do those side missions again........

One you complete the side missions they are done for good. I completed them all (except the last one because it's bugged) then reset the main quest. They stayed completed.