Subject: How fast 'can' we go?

I am writing a book where Id like to make a half way reasonable attempt at 
making it to another star system. Science fiction of course.. I've done 
some math on some possibilities, and I've decided without more 
information which I can't seem to find, I'm stuck. But, I want to base it on 
scientific fact. I dont want to write about something that is totally ridiculous 
scientifically, and we've all heard of enough 'warp drives' and 'hyperdirves' 
and all those wonderful machines. 
 
I was wondering if it is theoretically possible to slingshot around a
star, or a dwarf star or some such super dense body. By common sense, 
if you can get good speeds by slingshotting around the moon, doing the 
same around something super dense would be proportionally faster. If 
there is anything like this that could be theoretically possible, Id very much
appreciate the knowledge of it. I'll save the fiction for getting something 
like this to occur.

My intention, is for a spacecraft to reach speeds that could get to a
different system within a few thousand years. I do realize this is
incredibly fast and quite possibly impossible, but I am open to any
suggestions. 
 
Thank you for your time in reading this, and I look forward to hearing
from you.

Re: How fast 'can' we go?