First thing you need to do is to scout out a restaurant or two that you think would benefit from your performing for them. Then you need to pan your approach. One simple way is to do it while you are scouting them out. Sit and have a meal or a drink and ask the waiter if they have ever had a magician in the restaurant before, ask what their busy time is, when families are usually there, etc...and then when leaving you can ask for the manager and speak to them and let them know who you are, what you do and ask if ypu might be able to come in one night for a 2 hour demo (absolutely free to the restaurant) to show them just what it is you do and are offering them. Make sure you do the initial greeting to the manager in a quiet time period and not when the restaurant is full and the staff are at wits end.
One suggestion as well is to ensure that they pay you directly from the restaurant and that you explain that you will not solicit or hustle for tips but rather will help to enhance the servers tips (otherwise the servers may resent you taking away their bread and butter) AND it looks good to your audience if they offer you a tip and you politely decline saying "thank you very much but the restaurant pays me a very good salary BUT if you really enjoyed yourselves perhaps you might add it to your servers instead". The servers will be telling everyone about you then!
If you are going to work in a family restaurant I also suggest you learn balloon animlas as the kids love to walk away with a souvenir.
I guess you read my sticky and it rubbed off on you