I've just started resturant work really, and it took me a year to get here.
In January I said to myself that by the end of the year I want to be in any restaurant, and after doing a few freebies and rejections I finally got in!
The best advice I can give you is to tell them that you'll give them a free try of your skills on their buisiest night/day so they can see what you do and how you can handle the situation.
Another thing that is important is ring them up before you go and tell them who you are and ask what the manager's/owner's name is, so when you go in you know who to ask for.
Also, if they do take you on don't charge them a stupid price. I won't say how much i charge but if you want to talk more about it PM me.
It is really hard to get in, but just keep going!
My last point is that if the restaurant says no, don't worry. This will happen at some point and its best you should know that.
Give them a buisness card and contact them again a few months later. They might have more money by this time or the owner might have changed or maybe now they need a gimmick and something to promote them.
Always remember to keep in touch and don't rest your hopes on this one restaurant, go to loads of them!
Hope this helps,
Simon_Magic