Hi Terry,
Security is relative. Your browser software (Internet Explorer, Firefox, Chrome or others) will provide a basic level of security. But if you're using public wifi, like at a Panera's, a skilled operator could spoof the Panera network and compromise your security. Wifi at a campground has similar exposures, but might be less likely to be frequented by the skilled operator looking to take over your computer.
Corporations often use a software protocol called Point-to-point Tunneling that creates a very secure connection even on a public network, but to the best of my knowledge, banks are not offering Tunneling to their online banking customers.
If you get a MiFi or Jetpack (with accompanying data plan) your computer will make a connection to the Verizon or AT&T or Sprint, or T-Mobile cellular data network with a much higher level of security than any public wifi. This is similar to the data connection you'd have with a smartphone, but it uses your computer. I would say this is your best option.