You'll obviously want as much traffic as possible. Therefore, you should be using both online and offline traffic methods, or you'll be leaving money on the table.
Magazines and other publications can provide you with a lot of traffic. If the offer you're promoting is targeted to a specific group of people, then there's likely a magazine or two that caters to that group. Placing an ad that leads them back to your website can be very effective.
You should also consider placing an ad in one of your free local newspapers. Small ad spaces can be quite effective. If you have the budget though, then you may want to use a larger ad. Advertising rates with different papers will vary dramatically. It may be better for you to start out advertising in a smaller newspaper to save money.
Don't forget that you need to pay attention to the section that your ad is placed in. You wouldn't exactly want to place an ad for some type of electronic product in the sports section.
If you have a car, you may even consider using it for advertisement purposes. You can do this by using a full or partial vehicle wrap. This is a considerable and semi-permanent investment, so you'll need to find a CPA offer that you're very serious about promoting.
If you don't want to make such a significant investment, there are other options you can look into. Window stickers can be effective. Another option would be to use a bumper sticker or two. You can even give these bumper stickers to other people in hopes that they put them on their car too.
A relatively unique offline advertising method you could employ is to give away free promotional items that have your website's URL on them. Promo items can be anything like t-shirts, baseball caps, or pens. Pens would be much less expensive, so you'd have no problem giving them away to everyone you came across.
Instead of passing out promotional items, you can also make up some fliers You can leave them on cars or even in suitable businesses if they allow you to. The main drawback of using fliers is that it's much less targeted though
and remember to always get an ok first from your affiliate manager