EBay does charge fees, but for the increased visibility you might want to consider it. As I recall the fee structure is pretty fair.
I don't know how many eyes see this forum, but I do know if I was in the market for a used bicycle frame I would probably check eBay, as I do with many purchases. I don't know if the cyclists that would be interested in purchasing this frame would be the same as me though. 🙂
Also, your success will depend on how many people look for frames during the week or so your auction will be available.
The listing fee if an item isn't sold is relatively low, so it may be worth a try for you, although you tend to get more looks if you have a good feedback rating, which takes time to develop.
If you think you can get as high a price with a smaller (more targetted) audience, then go for it. Unless you are in a hurry, try a few free options first, then if they don't work out, check out EBay and see if it gets you a reasonable return in a timely manner.
With EBay, and a PayPal account, you can also accept credit cards, which opens up your item to some buyers that don't have the cash available (another fee involved per transaction).